4.5 Article

Riemann-Hilbert problems and soliton solutions of nonlocal real reverse-spacetime mKdV equations

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INVERSE SCATTERING AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-SPACETIME NONLINEAR SCHRODINGER EQUATIONS

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Summary: This paper presents nonlocal reverse-spacetime PT-symmetric multicomponent nonlinear Schrodinger equations and their inverse scattering transforms and soliton solutions using the Riemann-Hilbert technique under a specific nonlocal group reduction. 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 soliton solutions are constructed for the presented nonlocal reverse-spacetime PT-symmetric NLS equations.

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