Chapter 20: Lax Representation, Solitons and Bäcklund Transformations

Soliton equations are special partial differential equations. They have a number of interesting properties such as a Lax representation, solvable by the inverse scattering method, infinite many conservation laws. They also admit Bäcklund transformations and Lie-Bäcklund symmetries. Most of them also pass the Painlevé test. Lax representations can also be found for some system of ordinary differential equations…