Resonant line wave soliton solutions and interaction solutions for (2+1)-dimensional nonlinear wave equation

Abstract

Based on the N-soliton solutions, the resonant line wave soliton and interaction solutions are derived through some constraints in the (2+1)-dimensional nonlinear wave equation. General resonant line wave soliton solutions are firstly presented and their changing routes are illustrated. Then, several interaction solutions including a nonlinear superposition of resonant line wave soliton with breather wave, a hybrid between resonant line wave soliton and lump wave are constructed via long-wave limit method and module resonant mechanism. The characteristics and properties of these interaction solutions are discussed analytically and graphically. Localized wave and interaction solutions of the nonlinear wave models have a great impact on oceanography and physics. The results may be useful in investigating the physical phenomena in shallow water waves and nonlinear optics.