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Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation

机译：修正的Hunter-Saxton方程的对称约简，精确解和守恒律

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摘要

We study a modified Hunter-Saxton equation from the Lie group-theoretic point of view. The Lie point symmetry generators of the underlying equation are derived. We utilize the Lie algebra admitted by the equation to obtain the optimal system of one-dimensional subalgebras of the Lie algebra of the equation. These subalgebras are then used to reduce the underlying equation to nonlinear third-order ordinary differential equations. Exact traveling wave group-invariant solutions for the equation are constructed by integrating the reduced ordinary differential equations. Moreover, using the variational method, we construct infinite number of nonlocal conservation laws by the transformation of the dependent variable of the underlying equation.
机译：我们从李群理论的角度研究修正的Hunter-Saxton方程。推导了基础方程的李点对称生成器。我们利用方程式所承认的李代数来获得方程李代数的一维子代数的最优系统。然后，这些子代数用于将基础方程简化为非线性三阶常微分方程。该方程的精确行波群不变解是通过归约化的常微分方程构建的。此外，使用变分方法，我们通过变换基础方程的因变量来构造无限数量的非局部守恒律。

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