Interactions among two-dimensional nonlinear localized waves and periodic wave solution for a novel integrable $$(2+1)$$-dimensional KdV equation
Interactions among two-dimensional nonlinear localized waves and periodic wave solution for a novel integrable $$(2+1)$$-dimensional KdV equation
复制标题
DOI：
10.1007/s11071-022-07785-w
复制
发表时间：
2022-08
影响因子：
5.6
通讯作者：
Xu-Ping Zhao;Fuzhong Pang;Hasi Gegen
中科院分区：
文献类型：
--
作者：
Xu-Ping Zhao;Fuzhong Pang;Hasi Gegen
本文首先从KP 3和KP 4组合方程（cKP 3 -4）的四线性形式出发，导出了其双线性Bäcklund变换.然后利用双线性Bäcklund变换得到了cKP 3 -4方程的M-呼吸子解，并证明了单呼吸子解的动力学性质.研究了两个呼吸子之间的共振相互作用，线孤子与呼吸子，线孤子与群块，呼吸子与群块。我们还研究了cKP 3 -4方程中两个线孤子与一个呼吸子/块的弹性相互作用和共振相互作用，以及一个线孤子与两个块的弹性相互作用。通过渐近分析，我们证明了非线性局域波之间的共振相互作用表现出融合、裂变、时间局域呼吸子和粗糙块现象。此外，通过应用速度共振机制，证明了cKP 3 -4方程的各种孤子分子，包括块孤子、呼吸子孤子和线孤子。最后，利用双线性Bäcklund变换，构造了cKP 3 -4方程的以Riemann θ函数表示的单周期波解.
In this paper, a bilinear Bäcklund 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 Bäcklund 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 Bäcklund transformation, the one-periodic wave solution expressed in terms of the Riemann theta function for the cKP3-4 equation is constructed.