A nonlocal nonlinear Schrödinger equation derived from a two-layer fluid model

Abstract

By applying a simple symmetry reduction on a two-layer liquid model, a nonlocal counterpart of it is obtained. Then, a general form of nonlocal nonlinear Schrodinger (NNLS) equation with shifted parity, charge conjugate and delayed time reversal is obtained by using multi-scale expansion method. Some kinds of elliptic periodic wave solutions of the NNLS equation, which become soliton solutions and kink solutions when the modulus is taken as unity, are obtained by using elliptic function expansion method. Some representative figures of these solutions are given and analyzed in detail. In addition, by carrying out the classical symmetry method on the NNLS equation, not only the Lie symmetry group but also the related symmetry reduction solutions are given.