Energy-Dependent Reflectionless Inverse Scattering

  • Yutaka Kamimura

    Tokyo University of Marine Science and Technology, Japan
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Abstract

We develop a reflectionless inverse scattering theory regarding an energy-dependent Schrödinger equation. A necessary and sufficient condition for scattering data to recover a pair of potentials of the equation is obtained, based upon a complex generalization of a representation of reflectionless potentials via the Hirota transformation. As an application, an inverse scattering method is established for finding -soliton solutions of a nonlinear evolution system that is an isospectral flow of the energy-dependent Schrödinger equation.

Cite this article

Yutaka Kamimura, Energy-Dependent Reflectionless Inverse Scattering. Publ. Res. Inst. Math. Sci. 58 (2022), no. 2, pp. 379–440

DOI 10.4171/PRIMS/58-2-5