Nonlinear Waves & Hamiltonian Systems

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, Amherst 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 MODELS
1: Introduction and Motivation
2: Linear Dispersive Wave Equations
3: Nonlinear Dispersive Wave Equations
PART II - KORTEWEG-DE VRIES (KDV) EQUATION
4: The Korteweg-de Vries (KdV) Equation
5: From Boussinesq to KdV - Boussinesq Solitons as KdV Solitons
6: Traveling Wave Reduction, Elliptic Functions, and Connections to KdV
7: Burgers and KdV-Burgers (KdVB) Equations - Regularized ShockWaves
8: A Final Touch From KdV: Invariances and Self-Similar Solutions
9: Spectral Methods
10: Bäcklund Transformation for the KdV
11: 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 MODELS
14: Another Class of Models: Nonlinear Klein-Gordon Equations
15: Additional Tools/Results for Klein-Gordon Equations
16: Klein-Gordon to NLS Connection - Breathers as NLS Solitons
17: Interlude: Numerical Considerations for Nonlinear Wave Equations
PART IV - THE NONLINEAR SCHRÖDINGER EQUATIONS
18: The Nonlinear Schrödinger (NLS) Equation
19: NLS to KdV Connection - Dark Solitons as KdV Solitons
20: Actions, Symmetries, Conservation Laws, Noether's Theorem, and all that
21: Applications of Conservation Laws - Adiabatic Perturbation Method
22: Numerical Techniques for NLS
23: Inverse Scattering Transform II - the NLS Equation*
24: The Gross-Pitaevskii (GP) Equation
25: Variational Approximation for the NLS and GP Equations
26: Stability Analysis in 1D
27: Multi-Component Systems
28: Transverse Instability of Solitons Stripes - Perturbative Approach
29: Transverse Instability of Dark Stripes - Adiabatic Invariant Approach
30: Vortices in the 2D Defocusing NLS
PART V - DISCRETE MODELS
31: The Discrete Klein-Gordon model
32: Discrete Models of the Nonlinear Schrödinger Type
33: From Toda to FPUT and Beyond