Rational solutions and interaction solutions for (2 + 1)-dimensional nonlocal Schrödinger equation*

Abstract

A chain of novel higher order rational solutions with some parameters and interaction solutions of a (2+1)-dimensional reverse space–time nonlocal Schrödinger (NLS) equation was derived by a generalized Darboux transformation (DT) which is derived by Taylor expansion and determinants. We obtained a series of higher-order rational solutions by one spectral parameter and we could get the periodic wave solution and three kinds of interaction solutions, singular breather and periodic wave interaction solution, singular breather and traveling wave interaction solution, bimodal breather and periodic wave interaction solution by two spectral parameters. We found a general formula for these solutions in the form of determinants. We also analyzed the complex wave structures of the dynamic behaviors and the effects of special parameters and presented exact solutions for the (2+1)-dimensional reverse space–time nonlocal NLS equation.