Semi-rational solutions for the (2+1)-dimensional nonlocal Fokas system

Abstract

The ( 2 + 1 ) -dimensional [ ( 2 + 1 ) d ] Fokas system is a natural and simple extension of the nonlinear Schrödinger equation (see Eq. (2) in Fokas, 1994). In this letter, we introduce its PT -symmetric version, which is called the ( 2 + 1 ) d nonlocal Fokas system. The N -soliton solutions for this system are obtained by using the Hirota bilinear method whereas the semi-rational solutions are generated by taking the long-wave limit of a part of exponential functions in the general expression of the N -soliton solution. Three kinds of semi-rational solutions, namely (1) a hybrid of rogue waves and periodic line waves, (2) a hybrid of lump and breather solutions, and (3) a hybrid of lump, breather, and periodic line waves are put forward and their rather complicated dynamics is revealed.