Interactions among two-dimensional nonlinear localized waves and periodic wave solution for a novel integrable (2+1)-dimensional KdV equation

In this paper, a bilinear Backlund transformation of the combined KP3 and KP4 (cKP3-4) equation is first derived based on its quadrilinear form. Then we obtain the M-breather solution of the cKP3-4 equation using the bilinear Backlund transformation and demonstrate the dynamics of one-breather solution. We study the resonant interactions between two breathers, the line soliton and breather, the line soliton and lump, the breather and lump. We also investigate the elastic and resonant interactions of two line solitons and a breather/lump, the elastic interaction of a line soliton and two lumps for the cKP3-4 equation. Through the asymptotic analysis, we demonstrate the resonant interactions among nonlinear localized waves exhibit fusion, fission, time-localized breather and rough lump phenomena. In addition, various soliton molecules consisting of lumps, breathers and line solitons for the cKP3-4 equation are demonstrated by applying the velocity resonance mechanism. Finally, using the bilinear Backlund transformation, the one-periodic wave solution expressed in terms of the Riemann theta function for the cKP3-4 equation is constructed.