Resumen de Inverse Scattering Transform and Dynamics of Soliton Solutions for Nonlocal Focusing Modified Korteweg-de Vries Equation

Xiao-Fan Zhang, Shou-Fu Tian, Jin-Jie Yang, Tian-Tian Zhang

• The Riemann–Hilbert problem is developed to study the general N-soliton solution of the nonlocal modified Korteweg-de Vries equation in this work. The key to proving this result is the analysis of the Riemann–Hilbert problem related to the Cauchy problem of the nonlocal modified Korteweg-de Vries equation. The general N-soliton solution is acquired by solving the Riemann–Hilbert problem of the nonlocal equation under the reflectionless case and the matrix forms of the soliton solutions are given. The abundant phenomena of the solutions corresponding to different eigenvalues are further analyzed, including bounded solutions, singular solutions, degenerate solution and kink solution. It is noticed that many abundant phenomena are not found in the local modified Korteweg-de Vries equation by using RH method. Finally, the propagation behaviors of the solution (including one-, two-, and three soliton) are observed, and the characteristic lines are further used to analyze the continuity and other phenomena of the solution.