Thomas J Bridges

Professor of Mathematics

Seminars and Conferences
  BAMC 2012
University College London, 27-29 March 2012.
  SIAM Nonlinear Waves and Coherent Structures
University of Washington, Seattle, 13-16 June 2012.

Minisymposium on "Hamiltonian & Symplectic Methods in the theory of nonlinear waves" 

  Nonlinear Waves in Fluids
Loughborough University, 12-14 September 2012.
  Workshop: Spectral analysis, stability and bifurcation in modern nonlinear physical systems
Banff International Research Station, Canada, 4-9 November 2012.
  Industrial and Computational Mathematics Seminar
University of Nottingham, 20 February 2013.
  IUTAM Symposium on Nonlinear Interfacial Wave Phenomena
Limassol, Cyprus, 14 to 18 April 2013.
  Conference: Geometric Mechanics and Control Theory
Indian Institute of Science, Bangalore, 19-31 August 2013.
  Theory of Water Waves
Isaac Newton Institute for Mathematical Sciences, 14 July to 8 August 2014.
  IMA Conference on Nonlinearity and Coherent Structures
University of Reading, 6-8 July 2011.
  British Applied Mathematics Colloquium 2011
University of Birmingham, 11-13 April 2011.
  PDE Seminar
Trinity College, Dublin, 15 February 2011.
  Fluid Dynamics Seminar
Imperial College, 02 February 2011.
  Seminar in Applied Mathematics
University of Birmingham, 03 December 2010.
  Applied Mathematics Seminar
University of Bergen, Norway, April 2010.
  Mathematics Seminar
University College Dublin, Ireland, February 2010.
  Nonlinear Waves and the Maslov Index
Mathematics Institute, University of Warwick, November 2009.
  Dynamical Systems Seminar
School of Mathematics, University of Manchester, 11 February 2009.
  Workshop on Large Amplitude Internal Waves
ICMS Edinburgh, 1-4 December 2008.
  Conference on Nonlinear PDEs
OxPDE, St Anne's College, Oxford University, 5 June 2008.
  Applied Dynamics and Geometric Mechanics
Mathematisches Forschungsinsitut Oberwolfach, Germany, 20-26 July 2008.
  Colloquium in Mathematics
University of Reading, Friday 15 February 2008.
  Pre-2008 events
  MaGiC 2005: Manifolds and Geometric Integration Colloquia,
in Ustaoset, Norway, 14-18 February.

Click here for
The Ustaoset Lecture Slides

  List of publications click here
  New book
Some recent papers and preprints
  TJB & D.J. Ratliff [2018] Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory, Phil. Trans. R. Soc. Lond. A (in press) Surrey Repository, final-form preprint
  TJB & D.J. Ratliff [2017] On the elliptic-hyperbolic transition in Whitham modulation theory, SIAM J. Appl. Math. (in press) Surrey Repository, final-form preprint
  C.J. Grudzien, TJB & C.K.R.T. Jones [2017] Geometric phase in the Hopf bundle and the stability of nonlinear waves, Physica D 334 4-18. Physica D website
  F. Chardard & TJB [2015] Transversality of homoclinic orbits, the Maslov index, and the symplectic Evans function, Nonlinearity 28 77-102   IOP website
  TJB [2014] Emergence of dispersion in shallow water hydrodynamics via modulation of uniform flow, J. Fluid Mech. 761 R1-R9   JFM website
  TJB [2013] A universal form for the emergence of the Korteweg-de Vries equation, Proc. Roy. Soc. Lond. A 469 20120707. Journal website
  M.R. Turner & TJB [2013] Nonlinear energy transfer between fluid sloshing and vessel motion, J. Fluid Mech 719 606-636   Preprint .pdf
  TJB, J. Pennant & S. Zelik [2014] Degenerate hyperbolic conservation laws with dissipation: reduction to and validity of a class of Burgers-type equations. Arch. Rat. Mech. Anal. 214 671-716   Preprint .pdf
  TJB [2012] Emergence of unsteady dark solitary waves from coalescing spatially-periodic patterns, Proc. Royal Soc. London A 468 3754-3803. Preprint .pdf
  M.R. Turner, H. Alemi Ardakani, & TJB [2014] Instability of sloshing motion in a vessel undergoing pivoted oscillations J. Fluids Structures 52 166-180   JFS website
  H. Alemi Ardakani, TJB & M.R. Turner [2012] Resonance in a model for Cooker's sloshing experiment, Eur. J. Mech. B/Fluids 36 25-38. Final form Preprint .pdf  
  TJB [2012] Geometric lift of paths of Hamiltonian equilibria and homoclinic bifurcation, Inter. J. Bif. & Chaos 22 1250304. Final form Preprint .pdf
  TJB & D.J. Needham [2011] Breakdown of the shallow water equations due to growth of the horizontal vorticity, J. Fluid Mech. 679 655-666. Final form Preprint .pdf   JFM Page
  H. Alemi Ardakani & TJB [2011] Shallow-water sloshing in vessels undergoing prescribed rigid-body motion in three dimensions, J. Fluid Mech. 667 474-519. Final form Preprint .pdf
  F. Dias, TJB & J.M. Dudley [2011] Rogue waves, Preprint Downloadable Preprint .pdf
Contact information:

Address: Department of Mathematics
University of Surrey
Surrey GU2 7XH
Telephone: +44 (0)1483 689642
Fax: +44 (0)1483 686071
Mail to:
Home page:
Local Weather:
2016-2017 Academic Year
Geometric Mechanics
Spring 2018
see SurreyLearn for course material
Curves and Surfaces
Autumn 2017
see SurreyLearn for course material
Grasshopper's Guide
to Research Interests
  Symplectic pattern formation -->
  Hopf, Grassmann and Stiefel manifolds
  Phase dynamics
  Stability of multi-periodic and quasiperiodic patterns
  Hamiltonian and Lagrangian PDEs
 Variational Principles
  Dynamical systems and Hamiltonian mechanics
  Symplectic geometry
  Any aspect of water waves
  Solitary waves and fronts
  Geometry of absolute and convective instabilities
  Equivariant symplectic maps
  Springer Lecture Notes in Mathematics website
  Clifford analysis and water waves
Book in preparation on:

Symplectic Pattern Formation

  Full table of contents to appear here soon!
  Multisymplectic structures
  Dimension breaking of patterns
  Multi-periodic patterns
  solitary waves and fronts
  geometric instability criteria
  geometry of patterns in oceanography
  multi-symplectic Melnikov theory
  applications to water waves
  energy cascading in conservative systems
  symplectic defects
  wave interactions
  phase dynamics