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 Schrodinger (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.