A linear equation associated with nonlinear wave equations which support solitons is analyzed. A complete set of solutions of this linear equation is described through the techniques of scattering theory. This set is used to construct an explicit representation of a Green's function for perturbation theory. The cases of the nonlinear Schrödinger and sine-Gordon equations are discussed in some detail.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics