Rational and semi‐rational solutions of a nonlocal (2 + 1)‐dimensional nonlinear Schrödinger equation

Abstract

We consider the fully parity-time (PT) symmetric nonlocal (2 + 1)-dimensional nonlinear Schrödinger (NLS) equation with respect to x and y. By using Hirota's bilinear method, we derive the N-soliton solutions of the nonlocal NLS equation. By using the resulting N-soliton solutions and employing long wave limit method, we derive its nonsingular rational solutions and semi-rational solutions. The rational solutions act as the line rogue waves. The semi-rational solutions mean different types of combinations in rogue waves, breathers, and periodic line waves. Furthermore, in order to easily understand the dynamic behaviors of the nonlocal NLS equation, we display some graphics to analyze the characteristics of these solutions. KEYWORDSrational wave, semi-rational wave, soliton wave, the nonlocal (2 + 1)-dimensional NLS equation MSC CLASSIFICATION 35C08; 35Q51; 35Q55Math Meth Appl Sci. 2019;42:6865-6877.wileyonlinelibrary.com/journal/mma

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