Inverse scattering and soliton solutions of nonlocal reverse-spacetime nonlinear Schrödinger equations

Ma, Wen-Xiu

doi:10.1090/proc/15174

Inverse scattering and soliton solutions of nonlocal reverse-spacetime nonlinear Schrödinger equations
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Proc. Amer. Math. Soc. 149 (2021), 251-263 Request permission

Abstract:

The paper presents nonlocal reverse-spacetime PT-symmetric multicomponent nonlinear Schrödinger (NLS) equations under a specific nonlocal group reduction, and generates their inverse scattering transforms and soliton solutions by the Riemann-Hilbert technique. The Sokhotski-Plemelj formula is used to determine solutions to a class of associated Riemann-Hilbert problems and transform the systems that generalized Jost solutions need to satisfy. A formulation of solutions is developed for the Riemann-Hilbert problems associated with the reflectionless transforms, and the corresponding soliton solutions are constructed for the presented nonlocal reverse-spacetime PT-symmetric NLS equations.

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