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New soliton solutions for a Kadomtsev-Petviashvili (KP) like equation coupled to a Schrödinger equation. (English) Zbl 1252.35226
Summary: 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.

MSC:
35Q35 PDEs in connection with fluid mechanics
35Q41 Time-dependent Schrödinger equations and Dirac equations
35C08 Soliton solutions
35C07 Traveling wave solutions
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