Elements of soliton theory
Abstract
The book presents an introduction to the theory of solitons, with emphasis on the background material and introductory concepts of current research trends. Connections between a nonlinear partial differential equation that exhibits soliton behavior (the Korteweg-de Vries equation) and a linear eigenvalue problem are indicated, and one-dimensional scattering theory and inverse scattering methods are discussed. The Korteweg-de Vries equation is then treated by inverse scattering techniques, and the other common soliton equations are introduced, including the modified Korteweg-de Vries equation, the sine-Gordon equation and the cubic Schroedinger equation. Applications of soliton equations in physical situations are considered, with attention given to shallow water waves, ion plasma waves, one-dimensional dislocation theory vortex filaments, and coherent optical pulse propagation. Backlund transformations for the Korteweg-de Vries and other evolution equations are presented, and soliton perturbation theory is examined in relation to the Korteweg-de Vries equation and the cubic Schroedinger equation.
- Publication:
-
New York
- Pub Date:
- 1980
- Bibcode:
- 1980wi...book...29L
- Keywords:
-
- Physics;
- Solitary Waves;
- Wave Equations;
- Coherent Light;
- Korteweg-Devries Equation;
- Linear Systems;
- Perturbation Theory;
- Potential Theory;
- Scattering;
- Schroedinger Equation;
- Transformations (Mathematics);
- Vortex Filaments;
- Physics (General)