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 [2021] Nonlinear Theory for Coalescing Characteristics in Multiphase Whitham Modulation Theory, J. Nonl. Sci 31 7   Springer JNS website
  T.J. Burchell & TJB [2022] Symplectic transversality and the Pego-Weinstein theory, Adv. in Maths. 406 108524 AiM website
  TJB, A. Kostianko, & G. Schneider [2020] A proof of validity for multiphase Whitham modulation theory, Proc. Roy. Soc. Lond. A 476 20200203   arXiv version .pdf
  TJB, A. Kostiank, & S.Zelik & [2021] Validity of the hyperbolic Whitham modulation equations in Sobolev spaces, J. Diff. Eqns 274 971-995 JDE website
  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, Proc. Roy. Soc. Lond. A 475 Issue 2224 Royal Society website (open access)
  TJB & D.J. Ratliff [2019] Krein signature and Whitham modulation theory: the sign of characteristics and the "sign characteristic", Stud. Appl. Math. 142 314-335, SAPM Website
  TJB [2019] The pressure boundary condition and the pressure as Lagrangian for water waves, Water Waves 1 131-143, WW Website
  D.J. Ratliff & TJB [2018] Reduction to modified KdV and its KP-like generalization via phase modulation, Nonlinearity 31 3794-3813, IOP Nonlinearity website
  TJB & D.J. Ratliff [2018] Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory, Phil. Trans. R. Soc. Lond. A 376 Issue 2117, Royal Society website
  TJB & D.J. Ratliff [2017] On the elliptic-hyperbolic transition in Whitham modulation theory, SIAM J. Appl. Math. 77 1989-2011, SIAM website
  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
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:
2019-2020 Academic Year
Geometric Mechanics
Spring 2020
see SurreyLearn for course material
Lagrangian Fluid Dynamics
Autumn 2019
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