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

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.