Resonance solitons, soliton molecules and hybrid solutions for a (2+1)-dimensional nonlinear wave equation arising in the shallow water wave

In this paper, a systematic study for a (2 + 1) -dimensional nonlinear wave equation is performed. Based on the Hirota bilinear method, N-soliton solutions are obtained. By combining the asymptotic analysis with restricting the parameters of the two-soliton, X-type solitons and Y-type solitons are derived. The hybrid solutions among Y-type soliton, breather solution and lump are presented. In the meanwhile, new bound state molecules including lump-soliton molecule, lump-breather molecule and breather molecule are investigated through mechanisms of velocity resonance and mode resonance. The dynamics of these hybrid solutions are analyzed by the symbolic computations and graphs ways.