论文标题
一类非线性波的组分类和精确解
Group classification and exact solutions of a class of nonlinear waves
论文作者
论文摘要
我们将新的组分类方法的扩展应用于由两个任意函数标记的非线性波方程家族，每个函数都取决于其自己的论点。获得的结果证实了所提出的小组分类方法的效率，称为不确定方法。从分类的第四阶拉格朗日方程组的模型方程式被选出。通过各种对称算子的相似性降低，后者的行进波解决方案是在二阶降低到二阶的普通微分方程中的相似性。多种方法还可以通过包括Lie grout和Hirota方法在内的多种方法找到多氧化解决方案和其他精确的解决方案。提供了整个对称组对任何给定解决方案的最通用动作。概述了整个研究中出现的拉格朗日方程式上的一些非凡事实。
We apply an extension of a new method of group classification to a family of nonlinear wave equations labelled by two arbitrary functions, each depending on its own argument. The results obtained confirm the efficiency of the proposed method for group classification, termed the method of indeterminates. A model equation from the classified family of fourth order Lagrange equations is singled out. Travelling wave solutions of the latter are found through a similarity reduction by variational symmetry operators, followed by a double order reduction into a second order ordinary differential equation. Multi-soliton solutions and other exact solutions are also found by various methods including Lie group and Hirota methods. The most general action of the full symmetry group on any given solution is provided. Some remarkable facts on Lagrange equations emerging from the whole study are outlined.
