N-soliton solutions for the nonlocal two-wave interaction system via the Riemann-Hilbert method

In this paper, a nonlocal two-wave interaction system from the Manakov hierarchy is investigated via the Riemann-Hilbert approach. Based on the spectral analysis of the Lax pair, a Riemann-Hilbert problem for the nonlocal two-wave interaction system is constructed. By discussing the solutions of this Riemann-Hilbert problem in both the regular and non-regular cases, we explicitly present the N-soliton solution formula of the nonlocal two-wave interaction system. Moreover, the dynamical behaviour of the single-soliton solution is shown graphically.