Reduction approach and three types of multi-soliton solutions of the shifted nonlocal mKdV equation

In this paper, a reduction approach is proposed for a shifted nonlocal mKdV equation, from which we obtain its three types of multi-soliton solutions. Specifically, we proceed with the general N - soliton solution of an AKNS (q, r) system in the form of Riemann-Hilbert formulation. Then, by imposing suitable parameter constraints such that the shifted nonlocal symmetry reduction condition is fulfilled, we succeed to reduce the N-soliton solution of the AKNS (q, r) system to three types of multi-soliton solutions of the shifted nonlocal mKdV equation, which are classified according to the spectrum configurations. Moreover, several specific solutions are theoretically and graphically investigated. The proposed reduction approach paves a way for calculating multi-soliton solutions of the shifted nonlocal mKdV equation, which does not involve complicated spectral analysis of the Lax pair of the equation.

Automated summary

In this paper, a reduction approach is proposed for calculating multi-soliton solutions of the shifted nonlocal mKdV equation. The approach successfully reduces the N-soliton solution of the AKNS (q, r) system to three types of multi-soliton solutions of the shifted nonlocal mKdV equation, which are classified based on the spectrum configurations. Moreover, specific solutions are investigated theoretically and graphically.