Abstract 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.

中文翻译：

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非局域复数逆时空 mKdV 方程的逆散射和孤子解

摘要 本文讨论了非局部复数逆时空多分量可积修正 Korteweg-de Vries (mKdV) 方程的逆散射变换。我们建立相关的黎曼-希尔伯特问题并通过 Sokhotski-Plemelj 公式确定它们的解。逆散射问题包括广义矩阵 Jost 解的 Gelfand-Levitan-Marchenko 型方程和势的恢复公式。当反射系数为零时，相应的 Riemann-Hilbert 问题会产生非局部复数反向时空 mKdV 方程的孤子解。