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

Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences Beijing 100190, China and School of Mathematical Sciences, University of Chinese Academy of Sciences - Beijing 100049, China

^(a) zyyan@mmrc.iss.ac.cn (corresponding author)

Received: 13 March 2017
Accepted: 31 July 2017

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.