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

作者：Ma, Wen-Xiu^*

来源：Journal of Geometry and Physics, 2020, 157: 103845.

DOI：10.1016/j.geomphys.2020.103845

• Reverse-spacetime nonlocal integrable equation
• Matrix spectral problem
• Inverse scattering transform
• Riemann-Hilbert problem
• Soliton solution

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.

• 单位
  西北大学; 浙江师范大学