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.

"...should find an enthusiastic following, and the author is to be congratulated on a job well done." American Scientist

"...a fine book, certainly the one that I would choose as the text for an introductory course on solitons." SIAM Review

"All things considered, I cannot think of a clearer introduction to the subject from a mathematical point of view." Physics Today

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