论文标题
广义Zakharov方程的谎言对称性和相似解决方案
Lie symmetries and similarity solutions for the generalized Zakharov equations
论文作者
论文摘要
谎言点对称性的理论用于研究具有两个未知参数的广义Zakharov系统。该系统还原为三维实际价值函数系统，在那里我们发现允许五个谎言点对称性。从结果点开始，我们将重点放在提供旅行波相似性转换的这些上。还可以集成减少的系统，同时我们与两个二阶非线性普通微分方程的系统保持在一起。后一个系统的参数被分类为顺式接收谎言点对称性的方程式。找到了精确的旅行波解决方案，而一维的Ermakov-Pinney方程可以描述广义的Zakharov系统。
The theory of Lie point symmetries is applied to study the generalized Zakharov system with two unknown parameters. The system reduces into a three-dimensional real value functions system, where we find that admits five Lie point symmetries. From the resulting point, we focus on these which provide travel-wave similarity transformation. The reduced system can be integrated while we remain with a system of two second-order nonlinear ordinary differential equations. The parameters of the latter system are classified in order the equations to admit Lie point symmetries. Exact travel-wave solutions are found, while the generalized Zakharov system can be described by the one-dimensional Ermakov-Pinney equation.
