Observation of resonant solitons and associated integrable properties for nonlinear waves

Abstract

This paper is concerned with the integrability of a (2+1)-dimensional nonlinear evolution equation. The Painlevé analysis proves that this equation possesses the Painlevé property. Other integrable properties, including the bilinear Bäcklund transformation, Bell-polynomial-typed Bäcklund transformation, Lax pairs and infinite conservation laws, are derived directly by virtue of the Hirota bilinear method and Bell polynomials. The general form of the resonant soliton solutions are constructed based on the linear superposition principle. The resonant two-soliton solutions consist of three waves, each of which is one-soliton profile. For the resonant three-soliton solutions, the resonance of waves may cause some waves to disappear or appear. We hope that the various resonant phenomena discussed here will be helpful to understand the propagation of nonlinear waves.