Inverse scattering and soliton solutions of nonlocal complex reverse-spacetime mKdV equations

摘要

The paper deals with the inverse scattering transforms for nonlocal complex reverse-spacetime multicomponent integrable modified Korteweg-de Vries (mKdV) equations. We establish associated Riemann-Hilbert problems and determine their solutions by the Sokhotski-Plemelj formula. The inverse scattering problems consist of Gelfand-Levitan-Marchenko type equations for the generalized matrix Jost solutions and the recovery formula for the potential. When reflection coefficients are zero, the corresponding Riemann-Hilbert problems yield soliton solutions to the nonlocal complex reverse-spacetime mKdV equations.

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