Thomas J. Bridges

List of Publications

  1. D. Avitabile & TJB [2010] Numerical implementation of complex orthogonalization, parallel transport on Stiefel bundles, and analyticity, Physica D (in press).

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

  3. 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.

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

  5. 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.

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

  7. 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.

  8. 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.

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

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

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

  12. 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.

  13. 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.

  14. 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.

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

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

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

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

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

  20. 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.

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

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

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

  24. 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.

  25. 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.

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

  27. 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.

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

  29. 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.

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

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

  32. 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.

  33. 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.

  34. 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.

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

  36. 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.

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

  38. 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.

  39. 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.

  40. 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).

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

  42. 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.

  43. 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.

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

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

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

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

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

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

  50. 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.

  51. 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.

  52. 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.

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

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

  55. 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.

  56. 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.

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

  58. 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.

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

  60. 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.

  61. 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.

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

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

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

  65. 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.

  66. 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.

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

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

  69. 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.

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

  71. 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.

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

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

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

  75. 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).

  76. 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.

  77. 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).

  78. 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.

  79. 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.

  80. 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.).

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

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

  83. 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.

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

  85. 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.

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

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

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

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

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

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

  92. 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.

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

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

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

  96. 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.

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

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

  99. 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

  100. 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.

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

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

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

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

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

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

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

  108. 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.

  109. 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.

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

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

  112. TJB [1982] A numerical simulation of large amplitude sloshing, in Proceedings of the 3rd International Conference on Numerical Ship Hydrodynamics, Edited by J.C. Dern & H.J. Haussling, pp. 269-284.