Breather, rational and semi-rational solutions of the generalized nonlocal Davey-Stewartson–type system

Abstract In this paper, the generalized nonlocal Davey-Stewartson–type system with PT-symmetry is studied, which can describe the nonlinear wave phenomenon in fluid, nonlinear optics and plasma physics. The soliton solutions are used to derive three types of breathers and breathers in the background of periodic line waves. With the aid of the method of long wave limit, the N -th–order rational solutions consisting of multiple lumps are constructed. Every single lump wave can present three types of structures, namely 1) bright lump, 2) four-petaled lump, and 3) dark lump. In addition, semi-rational solutions consisting of lumps, periodic line waves and breathers are obtained by using the partial long wave limit method. These new results enrich the structure of the nonlinear waves for the nonlocal Davey-Stewartson–type system.