New exact solutions for the (2 + 1)-dimensional generalized Broer–Kaup system

Abstract

The (1 + 1)-dimensional Broer–Kaup system, which describes the propagation of shallow water waves, is extended to a generalized (2 + 1)-dimensional model with Painleve property. In this paper, based on the general variable separation approach and two extended Riccati equations, we first find several new families of exact soliton-like solutions and periodic-like wave solutions with arbitrary functions for the (2 + 1)-dimensional simplified generalized Broer–Kaup (GBK) system ( B = 0). Abundant new localized excitations can be found by selecting appropriate functions. After that, we consider the conditions of ( B ≠ 0) to the GBK, and several new results are obtained.