论文标题
（2+1） - 二维KDV，第五阶KDV和Gardner方程，源自理想的流体模型。孤子，cNoidal和叠加溶液
(2+1)-dimensional KdV, fifth-order KdV, and Gardner equations derived from the ideal fluid model. Soliton, cnoidal and superposition solutions
论文作者
论文摘要
我们研究了（2+1）维情况下理想流体模型的重力表面波的问题。我们应用系统的过程来得出四个扩展参数的订单，幅度参数$α$，长波长参数$β$，横向波长参数$γ$和底部变量参数$δ$之间的给定关系。在这些参数之间关系的三种特殊情况下，我们得出了Korteweg-de Vries方程，第五阶KDV方程和Gardner方程的唯一可能的（2+1）维度扩展。所有这些方程都是非本地的。当底部平坦时，可以将（2+1）二维kdv方程转换为固定参考框架中的kadomtsev-petviashvili方程，在移动框架中的经典kp方程旁边。我们发现了（基本上是一维），发现了（2+1） - 维korteweg-de vries方程和kadomtsev-petviashvili方程。
We study the problem of gravity surface waves for an ideal fluid model in the (2+1)-dimensional case. We apply a systematic procedure to derive the Boussinesq equations for a given relation between the orders of four expansion parameters, the amplitude parameter $α$, the long-wavelength parameter $β$, the transverse wavelength parameter $γ$, and the bottom variation parameter $δ$. We derived the only possible (2+1)-dimensional extensions of the Korteweg-de Vries equation, the fifth-order KdV equation, and the Gardner equation in three special cases of the relationship between these parameters. All these equations are non-local. When the bottom is flat, the (2+1)-dimensional KdV equation can be transformed to the Kadomtsev-Petviashvili equation in a fixed reference frame and next to the classical KP equation in a moving frame. We have found soliton, cnoidal, and superposition solutions (essentially one-dimensional) to the (2+1)-dimensional Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation.
