Soliton solutions and strange wave solutions for (2＋1)-dimensional nonlocal nonlinear Schrödinger equation with PT-symmetric term

Abstract

In this paper, the fundamental (1＋1)-dimensional nonlinear Schrödinger equation is extended to a novel (2＋1)-dimensional nonlocal nonlinear Schrödinger (NNLS) equation with a PT-symmetric term. We obtain the 1-soliton solution, 2-soliton solution, breather wave and strange wave solution of the (2＋1)-dimensional NNLS equation via the Hirota bilinear method. Some obtained solutions describe the interactions between bright and breather waves propagating along the $y$-axis and long waves propagating along the $x$-axis. And the (2＋1)-dimensional NNLS equation has the PT-symmetry property and many conservation laws, it is worthy of being studied in nonlinear optics.