## Nonconservative Reflectionless Inverse Scattering and Soliton Solutions of an Associated Nonlinear Evolution System

J. Math. Sci. Univ. Tokyo
Vol. 28 (2021), No. 4, Page 651-712.

Kamimura, Yutaka
Nonconservative Reflectionless Inverse Scattering and Soliton Solutions of an Associated Nonlinear Evolution System
A nonconservative, reflectionless inverse scattering problem is discussed on an energy dependent Schrödinger equation. A scattering transform from the potential of the equation to the reflectionless scattering data is completely characterized by a function induced from a Gelfand-Levitan-Marchenko equation, with an expression of the inverse scattering transform in terms of the function. Based upon the inverse scattering theory, we establish an inverse scattering method by which $N$-soliton solutions of a nonlinear evolution system (Boussinesq system) are constructed.