Multi-soliton solutions for the positive coherently coupled NLS in the Kerr media via the Riemann–Hilbert approach

In this paper, we investigate the physically important positive coherently coupled nonlinear Schrödinger (NLS) system occurred in the nonlinear Kerr media, which corresponds to a 4-by-4 matrix Riemann–Hilbert (RH) problem. Based on the solutions to the nonregular RH problem with both simple zeros and second-order zeros, we present the corresponding multi-soliton solutions for the positive coherently coupled NLS system respectively. Moreover, we plot the graphics of the single-soliton and the two-breather-like soliton interactions in the simple zeros case. While in the second-zero case, the single-hump soliton, two-hump soliton as well as the interactions between two such solitons of this system are shown graphically, which reflect the fact that the multi-solitons of this positive coherently coupled NLS system admit phase sensitive property.