Thomas J. Bridges
List of Publications

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.

M.R. Turner & TJB [2019] Wetting and drying of twolayer shallowwater flow in a moving vessel via semiLagrangian simulation, European Journal of Mechanics B/Fluids (in press).

D.J. Ratliff & TJB [2018] Reduction to modified KdV and its KPlike generalization via phase modulation, Nonlinearity, 31 37943813.

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.

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.

TJB & D.J. Ratliff [2017] On the elliptichyperbolic transition in Whitham modulation theory, SIAM Journal of Applied Mathematics, 77 19892011.

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

C.J. Grudzien, TJB, & C.K.R.T. Jones [2016]
Geometric phase in the Hopf bundle and the stability of nonlinear waves,
Physica D,
334 418.

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

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

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

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

M.R. Turner & TJB [2016]
Timedependent conformal mapping of doublyconnected regions,
Advanced in Computational Mathematics,
42 947972.

M.R. Turner, TJB, & H. Alemi Ardakani [2016]
Lagrangian particle path formulation of multilayer shallowwater flows dynamically coupled to vessel motion,
Journal of Engineering Mathematics,
106 75106.

D.J. Ratliff & TJB [2016]
Whitham modulation equations, coalescing characteristics, and
dispersive Boussinesq dynamics,
Physica D,
333 107116.

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

H. Alemi Ardakani, TJB & M.R. Turner [2016]
Shallowwater sloshing in a moving vessel with variable crosssection
and wettingdrying using an extension of George's wellbalanced finite volume solver,
Journal of Computational Physics 314 590617.

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

TJB [2016]
Symmetry, Modulation, and Nonlinear Waves,
Book Chapter in LMS Lecture Notes
426 261283.

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).

H. Alemi Ardakani, TJB, & M.R. Turner [2016]
Adaptation of fwave finite volume methods to the twolayer
shallowwater equations in a moving vessel with a rigidlid,
Journal of Computational and Applied Mathematics 296 462479.

M.R. Turner, H. Alemi Ardakani, & TJB [2015]
The pendulumslosh problem: simulation using a timedependent conformal mapping,
Journal of Fluids and Structures
59 202223.

H. Alemi Ardakani, TJB, & M.R. Turner [2015]
Dynamic coupling between horizontal vessel motion and twolayer shallowwater sloshing,
Journal of Fluids and Structues 59 432460.

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

TJB [2015]
Breakdown of the Whitham modulation theory and the emergence of
dispersion, Studies in Applied Mathematics 135 277294.

TJB [2015] Book review of Homogeneous, Isotropic Turbulence: Phenomenology, Renormalization
and Statistical Closures by W. David McComb (OUP 2014). In
Contemporary Physics 56 397398.

F. Chardard & TJB [2015]
Transversality of homoclinic orbits, the Maslov index, and the symplectic Evans function, Nonlinearity 28 77102.

TJB [2014]
Emergence of dispersion in shallow water hydrodynamics via modulation of uniform flow, Journal of Fluid Mechanics 761 R1R9.

M.R. Turner, H. Alemi Ardakani, & TJB [2014]
Instability of sloshing motion in a vessel undergoing pivoted oscillations, Journal of Fluids and Structures 52 166180.

TJB [2015]
Dimension breaking from spatiallyperiodic patterns to KdV planforms, Journal of Dynamics and Differential Equations 27 443456.

TJB, J. Pennant & S. Zelik [2014]
Degenerate hyperbolic conservation laws with dissipation: reduction to and validity of
a class of Burgerstype equations, Archives for Rational Mechanics and Analysis214 671716.

TJB [2014]
Bifurcation from rolls to multipulse planforms via reduction to a parabolic Boussinesq model, Physica D275 818.

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

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

M.R. Turner & TJB [2013]
Nonlinear energy transfer between fluid sloshing and vessel motion, Journal of Fluid Mechanics 719 606636.

TJB [2012]
Emergence of unsteady dark solitary waves from
coalescing spatiallyperiodic patterns ,
Proceedings of the Royal Society of London A
468 37543803.

H. Alemi Ardakani, TJB & M.R. Turner [2012]
Resonance in a model for
Cooker's sloshing experiment,
European Journal of Mechanics B/ Fluids 36 2538.

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

H. Alemi Ardakani & TJB [2012]
Shallowwater sloshing in vessels undergoing prescribed rigidbody
motion in two dimensions,
European Journal of Mechanics B/ Fluids 31 3043.

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 13341344.

TJB & D.J. Needham [2011]
Breakdown of the shallow water equations due to growth
of the horizontal vorticity,
Journal of Fluid Mechanics 679 655666.

F. Dias, TJB & J.M. Dudley [2011]
Rogue waves, pages 295308 in
Environmental Hazards  the fluid dynamics of geophysics of extreme
events. Lecture Notes Series, National University of Singapore
21. Published by World Scientific Press.

H. Alemi Ardakani & TJB [2011]
Shallowwater sloshing in vessels undergoing prescribed rigidbody
motion in three dimensions,
Journal of Fluid Mechanics 667 474519.

TJB & N.M. Donaldson [2011]
Variational principles for water waves from the viewpoint of a
timedependent moving mesh,
Mathematika 57 147173.

TJB [2011] Book review of Solitons, Instantons, and Twistors
by M. Dunajski (CUP 2009). In
Contemporary Physics 52 174275.

H. Alemi Ardakani & TJB [2010]
Dynamic coupling between shallowwater sloshing and horizontal vehicle motion,
European Journal of Applied Mathematics 21 479517.

D. Avitabile & TJB [2010]
Numerical implementation of complex orthogonalization, parallel transport on Stiefel bundles, and analyticity,
Physica D 239 10381047.

TJB, P.E. Hydon & J.K. Lawson [2010]
Multisymplectic structures and the variational bicomplex,
Mathematical Proceedings of the Cambridge
Philosophical Society 148 159178.

F. Chardard, F. Dias & TJB [2009]
On the Maslov index of multipulse homoclinic orbits,
Proceedings of the Royal Society of London A
465 28972910.

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

F. Chardard, F. Dias & TJB [2009]
Computing the Maslov index of solitary waves. Part 1:
Hamiltonian systems on a fourdimensional phase space,
Physica D 238 18411867.

TJB [2009]
Wave breaking and the surface velocity field for threedimensional water waves,
Nonlinearity 22 947953.

TJB & N.M. Donaldson [2009]
Criticality manifolds and their role in the generation of solitary waves for twolayer flow with a free surface,
European Journal of Mechanics B/Fluids
28 117126.

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 19471948.

TJB [2008]
Conservation laws in curvilinear coordinates: a short proof of Vinokur's Theorem using differential forms,
Applied Mathematics and Computation
202 882885.

TJB [2008]
Degenerate relative equilibria, curvature of the momentum map and
homoclinic bifurcation,
Journal of Differential Equations
244 16291674.

TJB & F. Dias [2007]
Enhancement of the BenjaminFeir instability with dissipation,
Physics of Fluids 19 104104.

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

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 1454514557.

TJB & N.M. Donaldson [2006]
Secondary criticality of water waves. Part 2.
Unsteadiness and the BenjaminFeir instability from the viewpoint of hydraulics,
Journal of Fluid Mechanics 565 419439.

TJB & N.M. Donaldson [2006]
Secondary criticality of water waves. Part 1. Definition, bifurcation and solitary waves,
Journal of Fluid Mechanics 565 381417.

TJB & S. Reich [2006]
Numerical methods for Hamiltonian PDEs,
Journal of Physics A: Mathematics and General 39 52875320.

TJB [2006]
Canonical multisymplectic structure on the total exterior algebra bundle,
Proceedings of the Royal Society of London A 462 15311551.

F. Dias & TJB [2006]
The numerical computation of freelypropagating timedependent irrotational water waves,
Fluid Dynamics Research 38 803830.

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

TJB & F.E. LainePearson [2005]
The longwave instability of shortcrested waves, via embedding in the oblique twowave interaction,
Journal of Fluid Mechanics 543 147182.

TJB [2005]
Potentially singular particle paths.
Appendix to P. Sclavounos. Nonlinear particle kinematics of ocean waves,
Journal of Fluid Mechanics 540 133142.

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

TJB, P.E. Hydon & S. Reich [2005]
Vorticity and symplecticity in Lagrangian fluid dynamics,
Journal of Physics A: Mathematics and General
38 14031418.

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, SpringerVerlag, pp. 2967.

TJB & E. Fan [2004]
Solitary waves, periodic waves, and a stability analysis for Zufiria's higherorder Boussinesq model
for shallow water waves,
Physics Letters A 326 381390.

TJB [2004]
Deformability, and the susceptibility of bright NLS solitons to transverse instability,
Proceedings of the Royal Society of London A 460
26052615.

TJB & F.E. LainePearson [2004]
Nonlinear counterpropagating waves, multisymplectic geometry, and the stability of standing waves,
SIAM Journal of Applied Mathematics 64 20962120.

TJB [2004]
Superharmonic instability, homoclinic torus bifurcation and breaking water waves,
Journal of Fluid Mechanics 505 153162.

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

TJB & G. Derks [2003]
Constructing the symplectic Evans matrix using maximallyanalytic individual vectors,
Proceedings of the Royal Society of Edinburgh 133 505526.

TJB [2003] Book review of Introduction to Symmetry Analysis by B.J. Cantwell (CUP 2002). In
International Journal of Numerical Modelling 16 557558.

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 239258.

L. Allen & TJB [2003]
Flow past a swept wing with a compliant surface: stabilizing the attachment line boundary layer,
Studies in Applied Mathematics 110, 333349.

TJB [2003]
Stability of solitary waves: geometry, symplecticity and threedimensionality,
Writeup of the Benjamin Memorial
Lecture in the Proceedings of 2001 WindoverWaves II Conference,
Edited by S.G. Sajjadi & J.C.R. Hunt, Horwood: Chichester, pp. 178188.

F.R. Austin & TJB [2003]
A bundle view of boundary value problems: generalizing the GardnerJones bundle,
J. Differential Equations
189, 412439.

TJB, G. Derks & G. Gottwald [2002]
Stability and instability of solitary waves of the fifthorder KdV equation: a numerical framework,
Physica D 172, 190216.

L. Allen & TJB [2002]
Numerical exterior algebra and the compound matrix method,
Numerische Mathematik 92, 197232.

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.

TJB & G Derks [2002]
Linear instability of solitary wave solutions of the Kawahara equation and its generalizations,
SIAM Journal of Mathematical Analysis 33, 13561378.

A.L. Afendikov & TJB [2002]
Spectral stability of pulse solutions to the GinzburgLandau equation and its generalizations,
Progress in Nonlinear Science v.1 Nizgnii Novgorod 2002,
pp. 173178. (Proceedings of the conference
in honour of Andronov's 100th Anniversary).

TJB & K. Georgiou [2002]
Computing global orbits of the forced spherical pendulum,
Physica D 165, 111.

P. Ashwin, M.V. Bartuccelli, TJB & S.A. Gourley [2002]
Travelling fronts for the KPP equation with spatiotemporal delay,
Z. angewandte Mathematik & Physik 53, 103122.

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 233234.

TJB & F.E. LainePearson [2001]
Multisymplectic relative equilibria, multiphase wavetrains and coupled NLS equations,
Studies in Applied Mathematics 107, 137155.

TJB & S Reich [2001]
Computing Lyapunov exponents on a Stiefel manifold,
Physica D 156, 219238

TJB & S Reich [2001]
Multisymplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity,
Physics Letters A 284, 184193.

TJB [2001]
Transverse instability of solitarywave states of the waterwave problem,
Journal of Fluid Mechanics 439, 255278.

TJB & S Reich [2001]
Multisymplectic spectral discretizations for the ZakharovKuznetsov and shallow water equations,
Physica D 152 491504.

TJB, F Dias & D Menasce [2001]
Steady threedimensional waterwave patterns on a finitedepth fluid,
Journal of Fluid Mechanics 436, 145175.

TJB & G. Derks [2001]
The symplectic Evans matrix, and the instability of solitary waves and fronts with symmetry,
Archive for Rational Mechanics & Analysis 156, 187.

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. 3238.

A.L. Afendikov & TJB [2001]
Instability of the HockingStewartson pulse and its implications for threedimensional Poiseuille flow,
Proceedings of the Royal Society of London A 457, 257272.

TJB & K.V. Georgiou [2001]
A transverse spinning double pendulum,
Chaos, Solitons & Fractals 12, 131144.

TJB [2000]
Universal geometric condition for the transverse instability of solitary waves,
Physical Review Letters 84, 26142617.

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, 3771.

TJB [1999]
A new framework for studying the stability of genus1 and genus2 KP patterns,
European Journal of Mechanics B/Fluids 18, 493500.

TJB [1999]
The OrrSommerfeld equation on a manifold,
Proceedings of the Royal Society of London A 455, 30193040.

L. Brevdo, TJB, F. Dias & P. Laure [1999]
Convectively unstably wave packets in a film flow on an inclined plane
International Symposium on Twophase flow modelling
and experimentation, Pisa, 2326 May, 1999.

TJB & G Derks [1999]
Hodge duality and the Evans function,
Physics Letters A 251, 363372.

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 378381.

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, 24272469.

TJB [1998]
Toralequivariant partial differential equations and quasiperiodic patterns,
Nonlinearity 11, 467500

TJB, J. E. Furter & A. Lahiri [1997]
Instability and bifurcation near the symplectic 1:4 resonance,
Dynamics and Stability of Systems 12, 271292

TJB [1997]
Poisson structure of the reversible 1:1 resonance,
Physica D 112, 4049.

L Brevdo & TJB [1997]
Local and global instabilities of spatially developing flows: cautionary examples,
Proceedings of the Royal Society of London A 453, 13451364.

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, 13651395.

L Brevdo & TJB [1997]
Absolute and convective instabilites of temporally oscillating flows,
Z. angewandte Mathematik & Physik 48, 290309.

TJB [1997]
Multisymplectic structures and wave propagation,
Mathematical Proceedings of the Cambridge Philosophical Society 121, 14790.

T B Benjamin & TJB [1997]
Reappraisal of the KelvinHelmholtz problem. Part 2: Interaction of the KelvinHelmholtz,
superharmonic and BenjaminFeir instabilities,
Journal of Fluid Mechanics 333, 32773.

T B Benjamin & TJB [1997]
Reappraisal of the KelvinHelmholtz problem. Part 1: Hamiltonian structure,
Journal of Fluid Mechanics 333, 30125.

TJB [1996]
Recent developments on wave instability,
in Nonlinear Mathematics and Applications
Proceedings of the EPSRC Spring School, Edited by P.J. Aston, pp. 205217.

L Brevdo & TJB [1996]
Absolute and convective instabilities of spatially periodic flows,
Philosophical Transactions of the Royal Society London A 354, 102764.

TJB & F. Dias [1996]
Spatially quasiperiodic capillarygravity waves,
Contemporary Mathematics 200, 3145 (Proceedings of the Luminy
Meeting on Water waves).

TJB & A Mielke [1996]
Instability of spatiallyperiodic states for a family of semilinear PDEs on an infinite strip,
Mathematische Nachtrichten 179, 525.

TJB [1996]
Hamiltonian structure of plane wave instabilities,
Fields Institute Communications 8, 1933.
(Proceedings of the Field's Institute Workshop on Conservative Systems and Quantum
Chaos, Edited by D. Rod).

TJB [1996]
Periodic patterns, linear instability, symplectic
structure and meanflow dynamics for 3D surface waves,
Philosophical Transactions of the Royal Society of London A 354, 533574.

TJB, R.H. Cushman & R.S. MacKay [1995]
Dynamics near an irrational collision of eigenvalues for symplectic mappings,
Fields Institute Communications 4, 6179.
(Proceedings of the Field's Institute Workshop on Normal Forms and Homoclinic Chaos,
Edited by W.F. Langford).

TJB, P. Christodoulides & F. Dias [1995]
Spatial bifurcations of capillarygravity interfacial waves when the phase and
group velocities are nearly equal,
Journal of Fluid Mechanics 295, 121158.

TJB [1995]
Multisymplectic 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. 123.

TJB [1995]
Symplecticity, reversibility & elliptic operators,
Progress Nonlinear Differential Equations 20, 120
(Proceedings of the Groningen Dynamical Systems Meeting, edited by H. Broer et al.).

TJB & A Mielke [1995]
A proof of the BenjaminFeir instability,
Archive for Rational Mechanics & Analysis 133, 145198.

TJB & A.J. Cooper [1995]
Spanwise modulation of streamwise rolls in rotating channel flow,
Quarterly Journal of Mechanics & Applied Mathematics 48, 257284.

TJB & G. Rowlands [1994]
Instability of spatially quasiperiodic states in the GinzburgLandau equation,
Proceedings of the Royal Society of London A 444, 347362.

F. Dias & TJB [1994]
Geometrical aspects of spatially periodic interfacial waves,
Studies in Applied Mathematics 93, 93132.

TJB & A.J. Cooper [1994]
Modulated rolls in rotating channel flow,
Proceedings of theWorkshop on
Transition, Turbulence \& Combustion held at
NASA Langley Research Center, SpringerVerlag
(Eds. M.Y. Hussaini & T.L. Jackson), pp. 165179.

TJB [1994] Hamiltonian spatial structure for threedimensional waterwaves in a moving frame of reference,
Journal of Nonlinear Science 4, 221251.

TJB [1994]
Geometric aspects of degenerate modulation equations,
Studies in Applied Mathematics 91. 125151.

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

TJB [1993]
On the bifurcation of periodq points in maps,
Dynamics & Stability of Systems 8, 147163

TJB & R.H. Cushman [1993]
Unipotent normal forms for symplectic maps,
Physica D 65, 211241.

TJB [1992] Spatial Hamiltonian structure, energy flux and the waterwave problem,
Proceedings of the Royal Society of London A 439, 297315.

TJB [1992]
Spatially quasiperiodic states in shear flows,
Proceedings of the Workshop on
Transition and Turbulence held at NASA Langley Research Center,
SpringerVerlag (Eds. M.Y. Hussaini, A. Kumar & C.L. Street), pp.
137145.

TJB [1992]
Hamiltonian bifurcations of the spatial structure for coupled nonlinear Schrodinger equations,
Physica D 57, 375394.

TJB [1991]
Stability of periodic solutions near a collision of eigenvalues of opposite signature,
Mathematical Proceedings of the Cambridge Philosophical Society
109, 375403.

TJB [1990] Bifurcation of Periodic Solutions
Near a Collision of Eigenvalues of Opposite Signature,
Math. Proc. Cambridge Philosophical Society 108, 575601.

TJB [1990] O(2)invariant Hamiltonians on C^4 and the (m,n) modeinteraction problem for
capillarygravity waves,
Studies in Applied Mathematics 82, 93120.

TJB & F. Dias [1990]
An analysis of twodimensional water waves based on O(2) Symmetry,
Nonlinear Analysis TMA 14, 733764.

F. Dias & TJB [1990]
The Third Harmonic Resonance
for CapillaryGravity Waves with O(2) Spatial Symmetry,
Studies in Applied Mathematics 82, 1335.

TJB [1989]
The Hopf bifurcation with symmetry for the NavierStokes equations in L_p$ with application
to plane Poiseuille flow,
Archive for Rational Mechanics & Analysis 106, 335376

G. Chen, TJB & J. Zhou [1988]
Minimizing the reflection of waves by surface impedance using
boundary elements and global optimization
Wave Motion 10 239255.

TJB [1988]
Strong internal resonance, Z_2+Z_2 Symmetry and Multiple Periodic Solutions,
SIAM Journal of Mathematical Analysis 19, 10151031.

TJB & P.J. Morris [1987]
Boundary layer stability calculations,
Physics of Fluids 30(11), 33513358.

TJB [1987]
Secondary bifurcation and change of type for threedimensional standing waves in finite depth,
Journal of Fluid Mechanics 179, 137153.

TJB, G. Chen & G. Crosta [1987]
Minimizing the reflection of electromagnetic waves by surface impedance,
Wave Motion 9, 1936.

TJB [1987]
On the secondary bifurcation of three dimensional standing surface waves,
SIAM Journal of Applied Mathematics 47, 4059.

TJB [1986]
Cnoidal standing waves and the transition to the travelling hydraulic jump,
Physics of Fluids 29, 28192827.

TJB & L. N. Vaserstein [1986]
The local evaluation of the derivative of a determinant,
Journal of Computational Physics 65, 107119.

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. 251256.

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, 141159.

TJB [1984]
Spectral calculations of the spatial stability of nonparallel boundary
layers,
AIAA Paper 840437, AIAA 22nd Aerospace Sciences Meeting.

TJB & P.J. Morris [1984]
Differential eigenvalues in which the parameter appears nonlinearly,
Journal of Computational Physics 55
437460.