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The aim of this book is to give a more systematic account for the bifurcation theory method of dynamical systems to find traveling wave solutions with an emphasis on singular waves and understand their dynamics for some classes of the well-posedness of nonlinear partial differential equations.
Main Contents :
Chapter 1. Traveling Wave Equations of Some Physical Models
Chapter 2. Basic Mathematical Theory of the Singular Traveling Wave Systems
Chapter 3. Bifurcations of Traveling Wave Solutions of Nonlinear Elastic Rod Systems
Chapter 4. Bifurcations of Traveling Wave Solutions of Generalized Camassa-Holm Equation
Chapter 5. Bifurcations of Traveling Wave Solutions of Higher Order Korteweg-De Vries Equations
Chapter 6. The Bifurcations of the Traveling Wave Solutions of K(m,n) Equation
Chapter 7. Kink Wave Solution Determined by a Parabola Solution of Planar Dynamical Systems
Chapter 8. Traveling Wave Solutions of Coupled Nonlinear Wave Equations
Chapter 9. Solitary Waves and Chaotic Behavior for a Class of Coupled Field Equations
Chapter 10. Bifurcations of Breather Solutions of Some Nonlinear Wave Equations
Chapter 11. Bounded Solutions of (n+1)-Dimensional Sine- and Sinh-Gordon Equations
Chapter 12. Exact Explicit Traveling Wave Solutions for Two Classes of (n+1)-Dimensional Nonlinear Wave Equations
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