Thomas J Bridges
Professor of Mathematics
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Seminars and Conferences | ||
| Upcoming events | |||
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Northumbria University Mathematics of Complex and Nonlinear Phenomena Seminar, 1 May 2024. | |||
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Satellite meeting of the Newton Institute on Dispersive Hydrodynamics, Northumbria University, 22 July to 16 August 2024. | |||
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Solitons, Collapses, and Turbulence (SCT-2024) Belgrade, Serbia, 1-5 July 2024. | |||
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SIAM Conference on Nonlinear Waves Baltimore, Maryland, 24-27 June 2024 | |||
| Previous notable events | |||
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Newton Institute for Mathematical Sciences 2022 Sixth month programme on Dispersive Hydrodynamics, July-December 2022. | |||
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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"
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Applied Mathematics Seminar University of Nottingham, 20 February 2013. | |||
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IUTAM Symposium on Nonlinear Interfacial Wave Phenomena Limassol, Cyprus, 14 to 18 April 2013. | |||
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Theory of Water Waves Isaac Newton Institute for Mathematical Sciences, 14 July to 8 August 2014. | |||
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IMA Conference on Nonlinearity and Coherent Structures University of Reading, 6-8 July 2011. | |||
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British Applied Mathematics Colloquium 2011 University of Birmingham, 11-13 April 2011. | |||
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PDE Seminar Trinity College, Dublin, 15 February 2011. | |||
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Fluid Dynamics Seminar Imperial College, 02 February 2011. | |||
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Seminar in Applied Mathematics University of Birmingham, 03 December 2010. | |||
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Applied Mathematics Seminar University of Bergen, Norway, April 2010. | |||
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Mathematics Seminar University College Dublin, Ireland, February 2010. | |||
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Nonlinear Waves and the Maslov Index Mathematics Institute, University of Warwick, November 2009. | |||
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Dynamical Systems Seminar School of Mathematics, University of Manchester, 11 February 2009. | |||
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Workshop on Large Amplitude Internal Waves ICMS Edinburgh, 1-4 December 2008. | |||
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Conference on Nonlinear PDEs OxPDE, St Anne's College, Oxford University, 5 June 2008. | |||
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Applied Dynamics and Geometric Mechanics Mathematisches Forschungsinsitut Oberwolfach, Germany, 20-26 July 2008. | |||
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Colloquium in Mathematics University of Reading, Friday 15 February 2008. | |||
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MaGiC 2005: Manifolds and Geometric Integration Colloquia, in Ustaoset, Norway, 14-18 February.
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| Blog on Research in Mathematics at the University of Surrey (click here) |
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Book on nonlinear waves |
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Some recent papers and preprints |
| TJB & T.J. Burchell & TJB [2024] Transverse instability of solitary waves, multisymplectic Dirac operators, and the Evans function, Draft manuscript | |
| A. Mansar, M.R. Turner, TJB, & F. Dias [2024] A theory for three-dimensional breaking water waves and white-capping in deep water, Draft manuscript | |
| 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. Kostianko, & 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 | |
| Complete list of publications (click here) | |
Contact information:
| Address: | Department of Mathematics |
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| University of Surrey Guildford Surrey GU2 7XH ENGLAND |
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| Telephone: | +44 (0)1483 689642 |
| Fax: | +44 (0)1483 686071 |
| Mail to: | t.bridges@surrey.ac.uk |
| Home page: | https://personalpages.surrey.ac.uk/t.bridges/ |
| Local Weather: click here |
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Lectures 2023-2024 Academic Year |
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MATM031 Nonlinear Patterns Autumn 2024 see SurreyLearn for course material |
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MAT3047 Lagrangian Fluid Dynamics Autumn 2023 see SurreyLearn for course material |
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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 |
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Book in
preparation on: Symplectic Pattern Formation |
| Table of contents | |
| 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 | |
| Wve interactions | |
| Phase dynamics | |
| Symplectic transversality | |
| Equivariant pattern formation |
