Professor Thomas J. Bridges

List of Publications

  1. TJB [2024] Book review of Wavefronts and rays as characteristics and asymptotics, 3rd edition, by A. Bona & M.A. Slawinski (World Scientific, 2020). In Contemporary Physics, CP webpage.

  2. Weipeng Hu, Zhengqi Han, TJB, & Zhijun Qiao [2023] Multi-symplectic simulations of W/M-shape-peaks solitons and cuspons for FORQ equation, Applied Mathematics Letters 145 145108772 (Elsevier webpage)

  3. P. Sprenger, TJB, & M. Shearer [2023] Traveling Wave Solutions of the Kawahara Equation Joining Distinct Periodic Waves, Journal of Nonlinear Science 33 79 (Springer website)

  4. H. Alemi Ardakani, & M.R. Turner [2023] A new physically realisable internal 1:1 resonance in the coupled pendulum-slosh system European Journal of Mechanics B/Fluids 98 180-193 (Elsevier website).

  5. TJB [2022] Book review of Mechanics of fluid deformations in rigid body rotations and plane channel Flow, by O.V. Troshkin (World Scientific, 2021). In Contemporary Physics, CP webpage.

  6. TJB & D.J. Ratliff [2022] Reappraisal of Whitham's 1967 theory for wave-mean flow interaction in shallow water, Wave Motion 115 103050 (arXiv version), (Published version).

  7. T.J. Burchell & TJB [2022] Symplectic transversality and the Pego-Weinstein theory, Advances in Mathematics 406 108524 AiM website .

  8. TJB & D.J. Ratliff [2021] Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory, Journal of Nonlinear Science 31 7 Springer JNS website .

  9. TJB, A. Kostianko, & S. Zelik [2021] Validity of the hyperbolic Whitham modulation equation in Sobolev spaces, Journal of Differential Equations 274 971-995 JDE website .

  10. TJB, A. Kostianko, & G. Schneider [2020] A proof of validity for multiphase Whitham modulation theory, Proceedings of the Royal Society of London A 476 20200203Royal Society website.

  11. TJB [2019] Book review of Classical Field Theory, by J. Franklin (Cambridge University Press, 2017). In Contemporary Physics, CP webpage.

  12. H. Alemi Ardakani, TJB, F. Gay-Balmaz, Y. Huang & C. Tronci [2019] A variational principle for fluid sloshing with vorticity, dynamically coupled to vessel motion, Proceedings of the Royal Society of London A 475 DOI .

  13. TJB & D.J. Ratliff [2019] Krein signature and Whitham modulation theory: the sign of characteristics and the "sign characteristic", Studies in Applied Mathematics, doi.org/10.1111/samp.12256.

  14. TJB [2019] The pressure boundary condition and the pressure as Lagrangian for water waves, Water Waves, DOI 10.1007/s42286-019-00001-0 (link).

  15. M.R. Turner & TJB [2019] Wetting and drying of two-layer shallow-water flow in a moving vessel via semi-Lagrangian simulation, European Journal of Mechanics B/Fluids, 76 153-165 (link).

  16. D.J. Ratliff & TJB [2018] Reduction to modified KdV and its KP-like generalization via phase modulation, Nonlinearity, 31 3794-3813.

  17. TJB [2018] Book review of The Many Faces of Maxwell, Dirac and Einstein Equations: a Clifford Bundle Approach, by W.A. Rodrigues Jr & E. Capelas de Oliveira (Springer, 2016). In Contemporary Physics, https://doi.org/10.1080/00107514.2018.1480528.

  18. TJB & D.J. Ratliff [2018] Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory, Philosophical Transactions of the Royal Society London A, 376 DOI 10.1098/rsta.2017.0194.

  19. TJB & D.J. Ratliff [2017] On the elliptic-hyperbolic transition in Whitham modulation theory, SIAM Journal of Applied Mathematics, 77 1989-2011.

  20. TJB [2017] Symmetry, Phase Modulation, and Nonlinear Waves, Cambridge University Press.

  21. C.J. Grudzien, TJB, & C.K.R.T. Jones [2016] Geometric phase in the Hopf bundle and the stability of nonlinear waves, Physica D, 334 4-18.

  22. TJB [2017] Book review of A Primer on Quantum Fluids by C.F. Barenghi & N. G. Parker (Springer, 2016). In Contemporary Physics, https://doi.org/10.1080/00107514.2017.1371238

  23. TJB [2017] Book review of Particles in the Coastal Ocean: Theory and Applications by D.R. Lynch, D.A. Greenberg, A. Bilgili, D.J. McGillicuddy, J.P. Manning, & A.L. Aretxabaleta (CUP 2015). In Contemporary Physics, http://dx.doi.org/10.1080/00107514.2017.1312539

  24. TJB [2017] Book review of Ray Tracing and Beyond: Phase Space Methods in Plasma Wave Theory by E.R. Tracy, A.J. Brizard, A.S. Richardson, & A.N. Kaufman (CUP 2014). In Contemporary Physics, http://dx.doi.org/10.1080/00107514.2017.1312534

  25. D.J. Ratliff & TJB [2016] Multiphase wavetrains, singular wave interactions and the emergence of the Korteweg-de Vries equation, Proceedings of the Royal Society of London A, 472 20160456.

  26. M.R. Turner & TJB [2016] Time-dependent conformal mapping of doubly-connected regions, Advanced in Computational Mathematics, 42 947-972.

  27. M.R. Turner, TJB, & H. Alemi Ardakani [2016] Lagrangian particle path formulation of multilayer shallow-water flows dynamically coupled to vessel motion, Journal of Engineering Mathematics, 106 75-106.

  28. D.J. Ratliff & TJB [2016] Whitham modulation equations, coalescing characteristics, and dispersive Boussinesq dynamics, Physica D, 333 107-116.

  29. TJB & D.J. Ratliff [2016] Double criticality and the two-way Boussinesq equation in stratified shallow water hydrodynamics, Physics of Fluids 28 062103.

  30. H. Alemi Ardakani, TJB & M.R. Turner [2016] Shallow-water sloshing in a moving vessel with variable cross-section and wetting-drying using an extension of George's well-balanced finite volume solver, Journal of Computational Physics 314 590-617.

  31. TJB, M.D. Groves, & D.P. Nicholls (Editors) [2016] Lectures on the Theory of Water Waves, LMS Lecture Notes 426 Cambridge University Press: Cambridge.

  32. TJB [2016] Symmetry, Modulation, and Nonlinear Waves, Book Chapter in LMS Lecture Notes 426 261-283.

  33. TJB, M.R. Turner, & H. Alemi Ardakani [2016] Modelling and analysis of floating ocean wave energy extraction devices, to appear in UK Success Stories in Industrial Mathematics, edited by P. Aston, T. Mulholland, K. Tant (in press).

  34. H. Alemi Ardakani, TJB, & M.R. Turner [2016] Adaptation of f-wave finite volume methods to the two-layer shallow-water equations in a moving vessel with a rigid-lid, Journal of Computational and Applied Mathematics 296 462-479.

  35. M.R. Turner, H. Alemi Ardakani, & TJB [2015] The pendulum-slosh problem: simulation using a time-dependent conformal mapping, Journal of Fluids and Structures 59 202-223.

  36. H. Alemi Ardakani, TJB, & M.R. Turner [2015] Dynamic coupling between horizontal vessel motion and two-layer shallow-water sloshing, Journal of Fluids and Structues 59 432-460.

  37. D.J. Ratliff & TJB [2015] Phase dynamics of periodic waves leading to the Kadomtsev-Petviashvili equation in 3+1 dimensions, Proceedings of the Royal Society of London A 471 20150137.

  38. TJB [2015] Breakdown of the Whitham modulation theory and the emergence of dispersion, Studies in Applied Mathematics 135 277-294.

  39. TJB [2015] Book review of Homogeneous, Isotropic Turbulence: Phenomenology, Renormalization and Statistical Closures by W. David McComb (OUP 2014). In Contemporary Physics 56 397-398.

  40. F. Chardard & TJB [2015] Transversality of homoclinic orbits, the Maslov index, and the symplectic Evans function, Nonlinearity 28 77-102.

  41. TJB [2014] Emergence of dispersion in shallow water hydrodynamics via modulation of uniform flow, Journal of Fluid Mechanics 761 R1-R9.

  42. M.R. Turner, H. Alemi Ardakani, & TJB [2014] Instability of sloshing motion in a vessel undergoing pivoted oscillations, Journal of Fluids and Structures 52 166-180.

  43. TJB [2015] Dimension breaking from spatially-periodic patterns to KdV planforms, Journal of Dynamics and Differential Equations 27 443-456.

  44. TJB, J. Pennant & S. Zelik [2014] Degenerate hyperbolic conservation laws with dissipation: reduction to and validity of a class of Burgers-type equations, Archives for Rational Mechanics and Analysis214 671-716.

  45. TJB [2014] Bifurcation from rolls to multi-pulse planforms via reduction to a parabolic Boussinesq model, Physica D275 8-18.

  46. M.R. Turner, TJB & H. Alemi Ardakani [2013] Dynamic coupling in Cooker's sloshing experiment with baffles, Physics of Fluids 25 112102.

  47. TJB [2013] A universal form for the emergence of the Korteweg-de Vries equation, Proceedings of the Royal Society of London A 469 20120707, doi:10.1098/rspa.2012.0707.

  48. M.R. Turner & TJB [2013] Nonlinear energy transfer between fluid sloshing and vessel motion, Journal of Fluid Mechanics 719 606-636.

  49. TJB [2012] Emergence of unsteady dark solitary waves from coalescing spatially-periodic patterns , Proceedings of the Royal Society of London A 468 3754-3803.

  50. H. Alemi Ardakani, TJB & M.R. Turner [2012] Resonance in a model for Cooker's sloshing experiment, European Journal of Mechanics B/ Fluids 36 25-38.

  51. TJB [2012] Geometric lift of paths of Hamiltonian equilibria and homoclinic bifurcation, International Journal of Bifurcation and Chaos 22 1250304 (9 pages).

  52. H. Alemi Ardakani & TJB [2012] Shallow-water sloshing in vessels undergoing prescribed rigid-body motion in two dimensions, European Journal of Mechanics B/ Fluids 31 30-43.

  53. F. Chardard, F. Dias & TJB [2011] Computing the Maslov index of solitary waves. Part 2: Phase space of dimension greater than four, Physica D 240 1334-1344.

  54. TJB & D.J. Needham [2011] Breakdown of the shallow water equations due to growth of the horizontal vorticity, Journal of Fluid Mechanics 679 655-666.

  55. F. Dias, TJB & J.M. Dudley [2011] Rogue waves, pages 295-308 in Environmental Hazards - the fluid dynamics of geophysics of extreme events. Lecture Notes Series, National University of Singapore 21. Published by World Scientific Press.

  56. H. Alemi Ardakani & TJB [2011] Shallow-water sloshing in vessels undergoing prescribed rigid-body motion in three dimensions, Journal of Fluid Mechanics 667 474-519.

  57. TJB & N.M. Donaldson [2011] Variational principles for water waves from the viewpoint of a time-dependent moving mesh, Mathematika 57 147-173.

  58. TJB [2011] Book review of Solitons, Instantons, and Twistors by M. Dunajski (CUP 2009). In Contemporary Physics 52 174-275.

  59. H. Alemi Ardakani & TJB [2010] Dynamic coupling between shallow-water sloshing and horizontal vehicle motion, European Journal of Applied Mathematics 21 479-517.

  60. D. Avitabile & TJB [2010] Numerical implementation of complex orthogonalization, parallel transport on Stiefel bundles, and analyticity, Physica D 239 1038-1047.

  61. TJB, P.E. Hydon & J.K. Lawson [2010] Multisymplectic structures and the variational bicomplex, Mathematical Proceedings of the Cambridge Philosophical Society 148 159-178.

  62. F. Chardard, F. Dias & TJB [2009] On the Maslov index of multi-pulse homoclinic orbits, Proceedings of the Royal Society of London A 465 2897-2910.

  63. TJB [2009] Degeneracy of the action-frequency map: a mechanism for homoclinic bifurcation of invariant tori, Physical Review E 79 066603.

  64. F. Chardard, F. Dias & TJB [2009] Computing the Maslov index of solitary waves. Part 1: Hamiltonian systems on a four-dimensional phase space, Physica D 238 1841-1867.

  65. TJB [2009] Wave breaking and the surface velocity field for three-dimensional water waves, Nonlinearity 22 947-953.

  66. TJB & N.M. Donaldson [2009] Criticality manifolds and their role in the generation of solitary waves for two-layer flow with a free surface, European Journal of Mechanics B/Fluids 28 117-126.

  67. TJB [2008] Book review of Waves in Oceanic and Coastal Waters by Leo H. Holthuijsen (CUP 2007). In Quarterly Journal of the Royal Meteorological Society 134 1947-1948.

  68. TJB [2008] Conservation laws in curvilinear coordinates: a short proof of Vinokur's Theorem using differential forms, Applied Mathematics and Computation 202 882-885.

  69. TJB [2008] Degenerate relative equilibria, curvature of the momentum map and homoclinic bifurcation, Journal of Differential Equations 244 1629-1674.

  70. TJB & F. Dias [2007] Enhancement of the Benjamin-Feir instability with dissipation, Physics of Fluids 19 104104.

  71. TJB & N.M. Donaldson [2007] Reappraisal of criticality for two-layer flows and its role in the generation of internal solitary waves, Physics of Fluids 19 072111.

  72. F. Chardard, F. Dias & TJB [2006] Fast computation of the Maslov index for hyperbolic linear systems with periodic coefficients, Journal of Physics A: Mathematics and General 39 14545-14557.

  73. TJB & N.M. Donaldson [2006] Secondary criticality of water waves. Part 2. Unsteadiness and the Benjamin-Feir instability from the viewpoint of hydraulics, Journal of Fluid Mechanics 565 419-439.

  74. TJB & N.M. Donaldson [2006] Secondary criticality of water waves. Part 1. Definition, bifurcation and solitary waves, Journal of Fluid Mechanics 565 381-417.

  75. TJB & S. Reich [2006] Numerical methods for Hamiltonian PDEs, Journal of Physics A: Mathematics and General 39 5287-5320.

  76. TJB [2006] Canonical multi-symplectic structure on the total exterior algebra bundle, Proceedings of the Royal Society of London A 462 1531-1551.

  77. F. Dias & TJB [2006] The numerical computation of freely-propagating time-dependent irrotational water waves, Fluid Dynamics Research 38 803-830.

  78. TJB [2005] Steady dark solitary waves emerging from wave-generated meanflow: the role of modulation equations, Chaos 15 037113.

  79. TJB & F.E. Laine-Pearson [2005] The long-wave instability of short-crested waves, via embedding in the oblique two-wave interaction, Journal of Fluid Mechanics 543 147-182.

  80. TJB [2005] Potentially singular particle paths. Appendix to P. Sclavounos. Nonlinear particle kinematics of ocean waves, Journal of Fluid Mechanics 540 133-142.

  81. TJB & N.M. Donaldson [2005] Degenerate periodic orbits and homoclinic torus bifurcation, Physical Review Letters 95 104301.

  82. TJB, P.E. Hydon & S. Reich [2005] Vorticity and symplecticity in Lagrangian fluid dynamics, Journal of Physics A: Mathematics and General 38 1403-1418.

  83. F. Dias & TJB [2005] Weakly nonlinear wave packets and the nonlinear Schrodinger equation, In: Nonlinear waves in fluids: Recent advances and modern applications, CISM Courses and Lectures 483, Springer-Verlag, pp. 29-67.

  84. TJB & E. Fan [2004] Solitary waves, periodic waves, and a stability analysis for Zufiria's higher-order Boussinesq model for shallow water waves, Physics Letters A 326 381-390.

  85. TJB [2004] Deformability, and the susceptibility of bright NLS solitons to transverse instability, Proceedings of the Royal Society of London A 460 2605-2615.

  86. TJB & F.E. Laine-Pearson [2004] Nonlinear counterpropagating waves, multi-symplectic geometry, and the stability of standing waves, SIAM Journal of Applied Mathematics 64 2096-2120.

  87. TJB [2004] Superharmonic instability, homoclinic torus bifurcation and breaking water waves, Journal of Fluid Mechanics 505 153-162.

  88. K.B. Blyuss, TJB & G. Derks [2003] Transverse instability and its long-term development for solitary waves of the (2+1)-Boussinesq equation, Physical Review E 67 056626.

  89. TJB & G. Derks [2003] Constructing the symplectic Evans matrix using maximally-analytic individual vectors, Proceedings of the Royal Society of Edinburgh 133 505-526.

  90. TJB [2003] Book review of Introduction to Symmetry Analysis by B.J. Cantwell (CUP 2002). In International Journal of Numerical Modelling 16 557-558.

  91. L. Allen & TJB [2003] Hydrodynamic stability of the Ekman boundary layer including interaction with a compliant surface: a numerical framework, European Journal Mechanics B/Fluids 22 239-258.

  92. L. Allen & TJB [2003] Flow past a swept wing with a compliant surface: stabilizing the attachment line boundary layer, Studies in Applied Mathematics 110, 333-349.

  93. TJB [2003] Stability of solitary waves: geometry, symplecticity and three-dimensionality, Write-up of the Benjamin Memorial Lecture in the Proceedings of 2001 Wind-over-Waves II Conference, Edited by S.G. Sajjadi & J.C.R. Hunt, Horwood: Chichester, pp. 178-188.

  94. F.R. Austin & TJB [2003] A bundle view of boundary value problems: generalizing the Gardner-Jones bundle, J. Differential Equations 189, 412-439.

  95. TJB, G. Derks & G. Gottwald [2002] Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework, Physica D 172, 190-216.

  96. L. Allen & TJB [2002] Numerical exterior algebra and the compound matrix method, Numerische Mathematik 92, 197-232.

  97. TJB & G. Derks [2002] Dimension breaking of gradient elliptic operators, Presented to Professor K. Kirchgassner on the occasion of his 70th birthday, at Kloster Irsee, January 2002.

  98. TJB & G Derks [2002] Linear instability of solitary wave solutions of the Kawahara equation and its generalizations, SIAM Journal of Mathematical Analysis 33, 1356-1378.

  99. A.L. Afendikov & TJB [2002] Spectral stability of pulse solutions to the Ginzburg-Landau equation and its generalizations, Progress in Nonlinear Science v.1 Nizgnii Novgorod 2002, pp. 173-178. (Proceedings of the conference in honour of Andronov's 100th Anniversary).

  100. TJB & K. Georgiou [2002] Computing global orbits of the forced spherical pendulum, Physica D 165, 1-11.

  101. P. Ashwin, M.V. Bartuccelli, TJB & S.A. Gourley [2002] Travelling fronts for the KPP equation with spatio-temporal delay, Z. angewandte Mathematik & Physik 53, 103-122.

  102. TJB [2002] Book review of Systems of Conservation Laws 2: Geometric Structures, Oscillation and Mixed Problems by D. Serre (CUP 2000). In Contemporary Physics 43 233-234.

  103. TJB & F.E. Laine-Pearson [2001] Multi-symplectic relative equilibria, multi-phase wavetrains and coupled NLS equations, Studies in Applied Mathematics 107, 137-155.

  104. TJB & S Reich [2001] Computing Lyapunov exponents on a Stiefel manifold, Physica D 156, 219-238

  105. TJB & S Reich [2001] Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity, Physics Letters A 284, 184-193.

  106. TJB [2001] Transverse instability of solitary-wave states of the water-wave problem, Journal of Fluid Mechanics 439, 255-278.

  107. TJB & S Reich [2001] Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations, Physica D 152 491-504.

  108. TJB, F Dias & D Menasce [2001] Steady three-dimensional water-wave patterns on a finite-depth fluid, Journal of Fluid Mechanics 436, 145-175.

  109. TJB & G. Derks [2001] The symplectic Evans matrix, and the instability of solitary waves and fronts with symmetry, Archive for Rational Mechanics & Analysis 156, 1-87.

  110. TJB & G. Derks [2001] The symplectic Evans matrix and solitary wave instability Proceedings of the Conference: Symmetry and Perturbation Theory 2001, Editors: D. Bambusi, G. Gaeta & M. Cadoni, World Scientific Ltd, pp. 32-38.

  111. A.L. Afendikov & TJB [2001] Instability of the Hocking-Stewartson pulse and its implications for three-dimensional Poiseuille flow, Proceedings of the Royal Society of London A 457, 257-272.

  112. TJB & K.V. Georgiou [2001] A transverse spinning double pendulum, Chaos, Solitons & Fractals 12, 131-144.

  113. TJB [2000] Universal geometric condition for the transverse instability of solitary waves, Physical Review Letters 84, 2614-2617.

  114. L Brevdo, P Laure, TJB, & F Dias [1999] Linear pulse structure and signalling in a film flow on an inclined plane, Journal of Fluid Mechanics 396, 37-71.

  115. TJB [1999] A new framework for studying the stability of genus-1 and genus-2 KP patterns, European Journal of Mechanics B/Fluids 18, 493-500.

  116. TJB [1999] The Orr-Sommerfeld equation on a manifold, Proceedings of the Royal Society of London A 455, 3019-3040.

  117. L. Brevdo, TJB, F. Dias & P. Laure [1999] Convectively unstably wave packets in a film flow on an inclined plane International Symposium on Two-phase flow modelling and experimentation, Pisa, 23-26 May, 1999.

  118. TJB & G Derks [1999] Hodge duality and the Evans function, Physics Letters A 251, 363-372.

  119. TJB [1999] Book review of Systems of Conservation Laws 1: Hyperbolicity, Entropies, Shock Waves by D. Serre (CUP 1999). In Journal of Fluid Mechanics 401 378-381.

  120. TJB & G Derks [1999] Unstable eigenvalues and the linearisation about solitary waves and fronts with symmetry, Proceedings of the Royal Society of London A 455, 2427-2469.

  121. TJB [1998] Toral-equivariant partial differential equations and quasiperiodic patterns, Nonlinearity 11, 467-500

  122. TJB, J. E. Furter & A. Lahiri [1997] Instability and bifurcation near the symplectic 1:4 resonance, Dynamics and Stability of Systems 12, 271-292

  123. TJB [1997] Poisson structure of the reversible 1:1 resonance, Physica D 112, 40-49.

  124. L Brevdo & TJB [1997] Local and global instabilities of spatially developing flows: cautionary examples, Proceedings of the Royal Society of London A 453, 1345-1364.

  125. TJB [1997] A geometric formulation of the conservation of wave action and its implications for signature and the classification of instabilities, Proceedings of the Royal Society of London A 453, 1365-1395.

  126. L Brevdo & TJB [1997] Absolute and convective instabilites of temporally oscillating flows, Z. angewandte Mathematik & Physik 48, 290-309.

  127. TJB [1997] Multi-symplectic structures and wave propagation, Mathematical Proceedings of the Cambridge Philosophical Society 121, 147-90.

  128. T B Benjamin & TJB [1997] Reappraisal of the Kelvin-Helmholtz problem. Part 2: Interaction of the Kelvin-Helmholtz, superharmonic and Benjamin-Feir instabilities, Journal of Fluid Mechanics 333, 327-73.

  129. T B Benjamin & TJB [1997] Reappraisal of the Kelvin-Helmholtz problem. Part 1: Hamiltonian structure, Journal of Fluid Mechanics 333, 301-25.

  130. TJB [1996] Recent developments on wave instability, in Nonlinear Mathematics and Applications Proceedings of the EPSRC Spring School, Edited by P.J. Aston, pp. 205-217.

  131. L Brevdo & TJB [1996] Absolute and convective instabilities of spatially periodic flows, Philosophical Transactions of the Royal Society London A 354, 1027-64.

  132. TJB & F. Dias [1996] Spatially quasiperiodic capillary-gravity waves, Contemporary Mathematics 200, 31-45 (Proceedings of the Luminy Meeting on Water waves).

  133. TJB & A Mielke [1996] Instability of spatially-periodic states for a family of semilinear PDEs on an infinite strip, Mathematische Nachtrichten 179, 5-25.

  134. TJB [1996] Hamiltonian structure of plane wave instabilities, Fields Institute Communications 8, 19-33. (Proceedings of the Field's Institute Workshop on Conservative Systems and Quantum Chaos, Edited by D. Rod).

  135. TJB [1996] Periodic patterns, linear instability, symplectic structure and mean-flow dynamics for 3D surface waves, Philosophical Transactions of the Royal Society of London A 354, 533-574.

  136. TJB, R.H. Cushman & R.S. MacKay [1995] Dynamics near an irrational collision of eigenvalues for symplectic mappings, Fields Institute Communications 4, 61-79. (Proceedings of the Field's Institute Workshop on Normal Forms and Homoclinic Chaos, Edited by W.F. Langford).

  137. TJB, P. Christodoulides & F. Dias [1995] Spatial bifurcations of capillary-gravity interfacial waves when the phase and group velocities are nearly equal, Journal of Fluid Mechanics 295, 121-158.

  138. TJB [1995] Multi-symplectic structures, Boussinesq equations and periodic travelling waves, Proceedings of the IUTAM/ISIMM Symposium on Nonlinear Waves in Fluids, Editors A. Mielke & K. Kirchgassner, World Scientific: Singapore, pp. 1-23.

  139. TJB [1995] Symplecticity, reversibility & elliptic operators, Progress Nonlinear Differential Equations 20, 1-20 (Proceedings of the Groningen Dynamical Systems Meeting, edited by H. Broer et al.).

  140. TJB & A Mielke [1995] A proof of the Benjamin-Feir instability, Archive for Rational Mechanics & Analysis 133, 145-198.

  141. TJB & A.J. Cooper [1995] Spanwise modulation of streamwise rolls in rotating channel flow, Quarterly Journal of Mechanics & Applied Mathematics 48, 257-284.

  142. TJB & G. Rowlands [1994] Instability of spatially quasiperiodic states in the Ginzburg-Landau equation, Proceedings of the Royal Society of London A 444, 347-362.

  143. F. Dias & TJB [1994] Geometrical aspects of spatially periodic interfacial waves, Studies in Applied Mathematics 93, 93-132.

  144. TJB & A.J. Cooper [1994] Modulated rolls in rotating channel flow, Proceedings of theWorkshop on Transition, Turbulence \& Combustion held at NASA Langley Research Center, Springer-Verlag (Eds. M.Y. Hussaini & T.L. Jackson), pp. 165-179.

  145. TJB [1994] Hamiltonian spatial structure for three-dimensional water-waves in a moving frame of reference, Journal of Nonlinear Science 4, 221-251.

  146. TJB [1994] Geometric aspects of degenerate modulation equations, Studies in Applied Mathematics 91. 125-151.

  147. TJB & J.E. Furter} [1993] Singularity Theory and Equivariant Symplectic Maps, Lecture Notes in Mathematics 1558, Springer-Verlag: Berlin (Research Monograph, 226 pages).

  148. TJB [1993] On the bifurcation of period-q points in maps, Dynamics & Stability of Systems 8, 147-163

  149. TJB & R.H. Cushman [1993] Unipotent normal forms for symplectic maps, Physica D 65, 211-241.

  150. TJB [1992] Spatial Hamiltonian structure, energy flux and the water-wave problem, Proceedings of the Royal Society of London A 439, 297-315.

  151. TJB [1992] Spatially quasiperiodic states in shear flows, Proceedings of the Workshop on Transition and Turbulence held at NASA Langley Research Center, Springer-Verlag (Eds. M.Y. Hussaini, A. Kumar & C.L. Street), pp. 137-145.

  152. TJB [1992] Hamiltonian bifurcations of the spatial structure for coupled nonlinear Schrodinger equations, Physica D 57, 375-394.

  153. TJB [1991] Stability of periodic solutions near a collision of eigenvalues of opposite signature, Mathematical Proceedings of the Cambridge Philosophical Society 109, 375-403.

  154. TJB [1990] Bifurcation of Periodic Solutions Near a Collision of Eigenvalues of Opposite Signature, Math. Proc. Cambridge Philosophical Society 108, 575-601.

  155. TJB [1990] O(2)-invariant Hamiltonians on C^4 and the (m,n) mode-interaction problem for capillary-gravity waves, Studies in Applied Mathematics 82, 93-120.

  156. TJB & F. Dias [1990] An analysis of two-dimensional water waves based on O(2) Symmetry, Nonlinear Analysis TMA 14, 733-764.

  157. F. Dias & TJB [1990] The Third Harmonic Resonance for Capillary-Gravity Waves with O(2) Spatial Symmetry, Studies in Applied Mathematics 82, 13-35.

  158. TJB [1989] The Hopf bifurcation with symmetry for the Navier-Stokes equations in L_p$ with application to plane Poiseuille flow, Archive for Rational Mechanics & Analysis 106, 335-376

  159. G. Chen, TJB & J. Zhou [1988] Minimizing the reflection of waves by surface impedance using boundary elements and global optimization Wave Motion 10 239-255.

  160. TJB [1988] Strong internal resonance, Z_2+Z_2 Symmetry and Multiple Periodic Solutions, SIAM Journal of Mathematical Analysis 19, 1015-1031.

  161. TJB & P.J. Morris [1987] Boundary layer stability calculations, Physics of Fluids 30(11), 3351-3358.

  162. TJB [1987] Secondary bifurcation and change of type for three-dimensional standing waves in finite depth, Journal of Fluid Mechanics 179, 137-153.

  163. TJB, G. Chen & G. Crosta [1987] Minimizing the reflection of electromagnetic waves by surface impedance, Wave Motion 9, 19-36.

  164. TJB [1987] On the secondary bifurcation of three dimensional standing surface waves, SIAM Journal of Applied Mathematics 47, 40-59.

  165. TJB [1986] Cnoidal standing waves and the transition to the travelling hydraulic jump, Physics of Fluids 29, 2819-2827.

  166. TJB & L. N. Vaserstein [1986] The local evaluation of the derivative of a determinant, Journal of Computational Physics 65, 107-119.

  167. TJB [1986] On the secondary bifurcation of standing surface waves in rectangular basins, Mathematics Applied to Fluids and Stability: Conference in honour of R.C. DiPrima, pp. 251-256.

  168. G. Chen & TJB [1985] Optimal boundary impedance for the minimization of reflection: (I) Asymptotic solutions by the geometrical optics method, Optimal Control: Applications & Methods 6, 141-159.

  169. TJB [1984] Spectral calculations of the spatial stability of non-parallel boundary layers, AIAA Paper 84-0437, AIAA 22nd Aerospace Sciences Meeting.

  170. TJB & P.J. Morris [1984] Differential eigenvalues in which the parameter appears nonlinearly, Journal of Computational Physics 55 437-460.