Multi-rational and semi-rational solitons and interactions for the nonlocal coupled nonlinear Schrödinger equations

Abstract

In this letter, we present a generalized Darboux transformation (gDT) for the nonlocal coupled nonlinear Schrödinger equations (nCNLS) with the aid of the loop group method. The associated N-fold Darboux transformation is given in terms of simple determinants. As a consequence, the novel N-th–order soliton solutions are found on the plane-wave background with only one spectral parameter. In particular, rational and semi-rational solutions are obtained such as vector generalization of the first- and second-order rational solutions, and interactions between rational solutions and periodic solutions. The results may be useful to explain the corresponding wave phenomena in nonlocal wave modes.