Similarity analysis of modified shallow water equations and evolution of weak waves
Similarity analysis of modified shallow water equations and evolution of weak waves
复制标题
修正浅水方程与弱波演化的相似性分析
DOI：
10.1016/j.cnsns.2011.06.011
复制
发表时间：
2012
影响因子：
3.9
通讯作者：
V. Sharma
中科院分区：
文献类型：
--
作者：
T. Sekhar;V. Sharma
本文利用控制系统的不变性群性质，得到了一类描述一维修正浅水方程的非线性偏微分方程组的精确解。给出了具有交换无穷小算子的点对称李群。利用对称发生器构造相似变量，将偏微分方程控制系统转化为常微分方程系统；在某些情况下，可以精确地解出这些方程。利用具有时空依赖性的控制系统的特解来研究弱不连续体的演化行为。
In this paper, we obtain exact solutions to the nonlinear system of partial differential equations (PDEs), describing the one dimensional modified shallow water equations, using invariance group properties of the governing system. Lie group of point symmetries with commuting infinitesimal operators, are presented. The symmetry generators are used for constructing similarity variables which lead the governing system of PDEs to system of ordinary differential equations (ODEs); in some cases, it is possible to solve these equations exactly. A particular solution to the governing system, which exhibits space–time dependence, is used to study the evolutionary behavior of weak discontinuities.