Rational and semi-rational solutions to the nonlocal Davey–Stewartson III equation

Abstract

We utilize the bilinear method and Kadomtsev–Petviashvili (KP) hierarchy reduction technique to obtain solutions for the nonlocal DS III equation. These solutions are elegantly expressed in terms of an N×N determinant, incorporating various parameter reduction constraints. It is important to note that these solutions are nontrivial and do not necessarily satisfy the local DS III equation. In the case of an even value of N, we derive solutions on constant backgrounds, while for odd values of N, solutions on periodic backgrounds are generated. To gain a deeper understanding of the dynamics involved, we conduct a thorough analysis of the derived solutions, accompanied by informative plots. Overall, our findings showcase the power of the bilinear method and KP hierarchy reduction technique in obtaining meaningful solutions for the nonlocal DS III equation, shedding light on its complex behavior and enriching our understanding of the system.