New soliton solutions for a Kadomtsev–Petviashvili (KP) like equation coupled to a Schrödinger equation

The repeated homogeneous balance is used to construct a new exact traveling wave solution of the Kadomtsev–Petviashvili (KP) like equation coupled to a Schrödinger equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions are successfully obtained, which contain rational and periodic-like solutions. This method is straightforward and concise, and it can be applied to other nonlinear evolution equations.