‘Partial Differential Equations and Solitary Waves Theory’ is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques arepresented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematicpresentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. Handles solitary waves theory in an accessible manner Combines in two parts an easy-to-read introduction with recent research achievements Graphs of all types of travelling waves illustrate the basic features of solitontheory INDICE: 1. Basic Concepts.- 2. First Order PDE.- 3. One-Dimensional Heat Flow.- 4. Higher Dimensional Heat Flow.- 5. One Dimensional Wave Equation.- 6. Higher Dimensional Wave Equation.- 7. Laplace's Equation.- 8. Nonlinear Equations.- 9. Physical Models.- 10. Numerical Applications.- 11. Solitons and Compactons.- 12. Solitary Wave Theory.- 13. The Family of the KdV Equations.- 14. KdV and mKdV Equations of Higher-Orders.- 15. Family of KdV-Type Equations.- 16. Boussinesq, Klein-Gordon and Liouville Equations.- 17. Burgers, Fisher and Related Equations.- 18. Camassa-Holm and Schrodinger Equations.
- ISBN: 978-3-642-00250-2
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 700
- Fecha Publicación: 01/05/2009
- Nº Volúmenes: 1
- Idioma: Inglés