论文标题
带有特殊溶液结构的新颖（2+1） - 二维集成KDV方程
A novel (2+1)-dimensional integrable KdV equation with peculiar solution structures
论文作者
论文摘要
著名的（1+1） - 二维Korteweg De-Vries（KDV）方程及其（2+1）二维扩展，Kadomtsev-petviashvili（KP）方程是物理科学中最重要的两个模型。 KP层次结构是通过KP方程的线性操作员明确编写的。通过组合第三个成员（KP3，通常的KP方程）和KP层次结构的第四个成员（KP4），获得了一种新颖的（2+1）-Dimension-demential KDV扩展，即CKP3-4方程。 CKP3-4方程的集成性由LAX对和双LAX对的存在来保证。在引入额外的辅助变量后，可以使用Hirota的双线性操作员使用CKP3-4系统通过使用双线性操作员进行双线性。 CKP3-4方程的精确解决方案具有某些特殊且有趣的属性，这些属性对于KP3和KP4方程无效。例如，孤子分子和缺失的D'Alembt类型解（任意依赖性速度向一个方向移动的任意行进波），包括周期性的扭结分子，周期性的扭结分子，几乎没有循环的孤子和包膜孤子，而不是用于CKP3-4方程的循环词素和包膜词素，而不是用于分离的方程和kp3方程。
The celebrated (1+1)-dimensional Korteweg de-Vries (KdV) equation and its (2+1)-dimensional extention, the Kadomtsev-Petviashvili (KP) equation, are two of the most important models in physical science. The KP hierarchy is explicitly written out by means of the linearized operator of the KP equation. A novel (2+1)-dimensional KdV extension, the cKP3-4 equation, is obtained by combining the third member (KP3, the usual KP equation) and the fourth member (KP4) of the KP hierarchy. The integrability of the cKP3-4 equation is guaranteed by the existence of the Lax pair and dual Lax pair. The cKP3-4 system can be bilinearized by using Hirota's bilinear operators after introducing an additional auxiliary variable. Exact solutions of the cKP3-4 equation possess some peculiar and interesting properties which are not valid for the KP3 and KP4 equations. For instance, the soliton molecules and the missing D'Alembert type solutions (the arbitrary travelling waves moving in one direction with a fixed model dependent velocity) including periodic kink molecules, periodic kink-antikink molecules, few cycle solitons and envelope solitons are existed for the cKP3-4 equation but not for the separated KP3 equation and the KP4 equation.
