Published: January 1981
... This book provides an entirely self-contained exposition on the subject ... The theory is presented in a mathematically satisfactory way and the treatment is fully rigorous, filling many gaps in the existing literature and presenting new insights into various aspects of the theory.
- 1. The Korteweg-De Vries Equation. 2. Solution by the Method of Gardner-Greene-Kruskal-Miura: The Inverse Scattering Transformation. 3. Isospectral Potentials. The Lax Approach. 4. Direct and Inverse Scattering for the Schrödinger Equation. 5. Direct and Inverse Scattering for the Generalized Zakharov-Shabat System. 6. Applications of the Inverse Scattering Transformation. 7. Perturbations. References.