Nonlinear Waves & Hamiltonian Systems

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