一类(2 + 1)维KdV方程的精确解及动力学性态
Dynamical Behaviors and Solutions of a Class of (2 + 1)-Dimensional KdV Equations
摘要: 本文利用指数函数法构造广义二维变系数KdV方程新精确解，并使用Mathematica软件描绘解的图像，分析解的性态。获取KdV型方程新的精确解，观察各个参数对波的影响，分析各个因素对水波传播状态的影响程度，为浅水背景下水波的传播问题提供一定参考。
Abstract:
In this thesis, new exact solutions to generalized two dimensional KdV equation with variable coefficients were constructed with exp-function method and homogeneous balance method, and graphic representation of the solutions was obtained and properties of the solutions were analyzed with Mathematica software. With new exact solutions to KdV equations obtained, the influence of each parameter on waves was observed and the degree to which each factor influences the propagation state of water waves was analyzed, which provided certain reference to problems regarding the propagation of water waves under shallow-water background.
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