Solitons: An Introduction

ISBN-13: 9780521336550 / Angielski / Miękka / 1989 / 240 str.

P. G. Drazin; R. S. Johnson; D. G. Crighton

Opis

Solitons: An Introduction discusses the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences. Drazin and Johnson explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering Tranform. Their aim is to present the essence of inverse scattering clearly, rather than rigorously or completely. Thus, the prerequisites are merely what is found in standard courses on mathematical physics 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 their solution, are given at the end of the book. Sections and exercises that contain more difficult material are indicated by asterisks.

Recenzje

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

Spis treści

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.