Solitons
An Introduction

This textbook is an introduction to the theory of solitons in the physical sciences.

P. G. Drazin (Author), R. S. Johnson (Author)

9780521336550, Cambridge University Press

Paperback, published 9 February 1989

240 pages
22.9 x 15.2 x 1.4 cm, 0.36 kg

"...an excellent book, achieving its goals both concisely and comprehensively." John G. Harris, Applied Mechanics Review

This textbook is an introduction to the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences. The authors explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering Transform. Their aim is to present the essence of inverse scattering clearly, rather than rigorously or completely. Thus, the prerequisites (i.e., partial differential equations, calculus of variations, Fourier integrals, linear waves and Sturm–Liouville theory), and more advanced material is explained in the text with useful references to further reading given at the end of each chapter. Worked examples are frequently used to help the reader follow the various ideas, and the exercises at the end of each chapter not only contain applications but also test understanding. Answers, or hints to the solution, are given at the end of the book. Sections and exercises that contain more difficult material are indicated by asterisks.

Preface
1. The Kortewag–de Vries equation
2. Elementary solutions of the Korteweg–de Vries equation
3. The scattering and inverse scattering problems
4. The initial-value problem for the Korteweg–de Vries equation
5. Further properties of the Korteweg–de Vries equation
6. More general inverse methods
7. The Painlevé property, perturbations and numerical methods
8. Epilogue
Answers and hints
Bibliography and author index
Motion picture index
Subject index.

Subject Areas: Applied mathematics [PBW]