Nonlinear Waves & Hamiltonian Systems From One To Many Degrees of Freedom, From Discrete To Continuum
, by Carretero-González, Ricardo; Frantzeskakis, Dimitrios J.; Kevrekidis, Panayotis G.
- ISBN: 9780192843241 | 0192843249
- Cover: Paperback
- Copyright: 2/5/2025
Ricardo Carretero-González, Professor, Department of Mathematics and Statistics, San Diego State University,Dimitrios J. Frantzeskakis, Professor, Department of Physics, National and Kapodistrian University of Athens, Panayotis G. Kevrekidis, Distinguished University Professor, University of Massachusetts, Amherst
Ricardo Carretero-González holds a Summa Cum Laude B.Sc. in Physics from the Universidad Nacional Autónoma de México, and a Ph.D. in Applied Mathematics and Computation from Queen Mary College, University of London. He previously held a post-doctoral post at University College London and at Simon Fraser University, Canada, and is currently a Professor of Applied Mathematics at San Diego State University. His research focuses on spatio-temporal dynamical systems, nonlinear waves, and their applications. He is an active advocate of the dissemination of science and he regularly delivers engaging presentations at local high schools and science festivals.
Dimitrios J. Frantzeskakis holds an Electrical Engineering Diploma from the University of Patras, and a PhD in Engineering from the National Technical University of Athens. He was an Instructor in the Naval Academy of Greece, a Research Associate at NTUA, and is currently a Professor in the Department of Physics at the National and Kapodistrian University of Athens. His research focuses on nonlinear waves and solitons, with applications to various physical contexts. Many of his theoretical results initiated important experimental projects, which verified a number of theoretical predictions reported in his papers; he is a co-author of several works reporting these experimental results.
Panayotis G. Kevrekidis holds a Distinguished University Professorship at the University of Massachusetts since 2015. Previously, he was an Assistant (2001-2005), Associate (2005-2010) and Full Professor (2010-2015) at UMass. His doctoral studies were conducted at Rutgers University, where he earned an M.S., an M. Phil. and a Ph.D. He subsequently spent a post-doctoral year between Princeton's Program in Applied and Computational Mathematics and Los Alamos' Center for Nonlinear Studies.
Ricardo Carretero-González holds a Summa Cum Laude B.Sc. in Physics from the Universidad Nacional Autónoma de México, and a Ph.D. in Applied Mathematics and Computation from Queen Mary College, University of London. He previously held a post-doctoral post at University College London and at Simon Fraser University, Canada, and is currently a Professor of Applied Mathematics at San Diego State University. His research focuses on spatio-temporal dynamical systems, nonlinear waves, and their applications. He is an active advocate of the dissemination of science and he regularly delivers engaging presentations at local high schools and science festivals.
Dimitrios J. Frantzeskakis holds an Electrical Engineering Diploma from the University of Patras, and a PhD in Engineering from the National Technical University of Athens. He was an Instructor in the Naval Academy of Greece, a Research Associate at NTUA, and is currently a Professor in the Department of Physics at the National and Kapodistrian University of Athens. His research focuses on nonlinear waves and solitons, with applications to various physical contexts. Many of his theoretical results initiated important experimental projects, which verified a number of theoretical predictions reported in his papers; he is a co-author of several works reporting these experimental results.
Panayotis G. Kevrekidis holds a Distinguished University Professorship at the University of Massachusetts since 2015. Previously, he was an Assistant (2001-2005), Associate (2005-2010) and Full Professor (2010-2015) at UMass. His doctoral studies were conducted at Rutgers University, where he earned an M.S., an M. Phil. and a Ph.D. He subsequently spent a post-doctoral year between Princeton's Program in Applied and Computational Mathematics and Los Alamos' Center for Nonlinear Studies.
PART I - INTRODUCTION AND MOTIVATION OF MODELS1. Introduction and Motivation2. Linear Dispersive Wave Equations3. Nonlinear Dispersive Wave EquationsPART II - KORTEWEG-DE VRIES (KDV) EQUATION4. The Korteweg-de Vries (KdV) Equation5. From Boussinesq to KdV - Boussinesq Solitons as KdV Solitons6. Traveling Wave Reduction, Elliptic Functions, and Connections to KdV7. Burgers and KdV-Burgers (KdVB) Equations - Regularized ShockWaves8. A Final Touch From KdV: Invariances and Self-Similar Solutions9. Spectral Methods10. Bäcklund Transformation for the KdV11. Inverse Scattering Transform I - the KdV equation*12. Direct Perturbation Theory for Solitons*13. The Kadomtsev-Petviashvili Equation*PART III - KLEIN-GORDON, SINE-GORDON, AND PHI-4 MODELS14. Another Class of Models: Nonlinear Klein-Gordon Equations15. Additional Tools/Results for Klein-Gordon Equations16. Klein-Gordon to NLS Connection - Breathers as NLS Solitons17. Interlude: Numerical Considerations for Nonlinear Wave EquationsPART IV - THE NONLINEAR SCHRÖDINGER EQUATIONS18. The Nonlinear Schrödinger (NLS) Equation19. NLS to KdV Connection - Dark Solitons as KdV Solitons20. Actions, Symmetries, Conservation Laws, Noether's Theorem, and all that21. Applications of Conservation Laws - Adiabatic Perturbation Method22. Numerical Techniques for NLS23. Inverse Scattering Transform II - the NLS Equation*24. The Gross-Pitaevskii (GP) Equation25. Variational Approximation for the NLS and GP Equations26. Stability Analysis in 1D27. Multi-Component Systems28. Transverse Instability of Solitons Stripes - Perturbative Approach29. Transverse Instability of Dark Stripes - Adiabatic Invariant Approach30. Vortices in the 2D Defocusing NLSPART V - DISCRETE MODELS31. The Discrete Klein-Gordon model32. Discrete Models of the Nonlinear Schrödinger Type33. From Toda to FPUT and Beyond
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