Some reverse space(RS) rational solutions for the nonlocal coupled nonlinear Schrödinger equations on the plane wave backgrounds

Abstract

A number of integrable nonlocal nonlinear Schrödinger (NNLS) type systems have been recently proposed. In this letter, a Darboux transformation (DT) of the nonlocal coupled nonlinear Schrödinger (NCNLS) equations is presented with the aid of the loop group method. The associated N-fold Darboux transformation is given on plane wave backgrounds. Starting from a special reverse space (RS) Lax pairs, the NCNLS equations are constructed, then we obtain one-, two- and N-soliton solution formulas of the NCNLS equations with N-fold Darboux transformation. As a consequence, two kinds of RS solutions are derived from plane wave backgrounds. Some novel soliton solutions and rational solutions are derived with the nonzero seed solutions through complex computations, including the bright soliton, kink soliton and breather wave soliton. The results may be useful to explain the corresponding wave phenomena in nonlocal wave modes.