The Hybrid and Interaction Solutions with Resonance Y-Type Solitons for the (2 + 1)-Dimensional KdV Equation

Abstract

The hybrid solutions and interaction solutions with resonance Y-type solitons are mainly investigated for the (2 + 1)-dimensional Korteweg-de Vries (KdV) equation, concerning lumps, resonance Y-type solitons and interaction solutions. Firstly, by the Hirota bilinear form, we deduce the periodic solitary wave solutions through modified three-wave method. Consequently, the lumps are gained in virtue of the parameter limit approach. Secondly, when applying some constraint conditions to the N-solitons, the resonance Y-type solitons are obtained. They are new types of soliton solutions for this system. Thirdly, adding other constraint conditions to the resonanceY-type solitons, the novel interaction phenomena of resonanceY-type solitons with breathers, and resonanceY-type solitons with the lumps arise. Finally, two types of hybrid solutions are obtained for this system, including the solitons, breathers and lumps; resonance Y-type solitons, breathers and lumps, respectively.