论文标题
抑制非线性波方程的保护定律和变异结构
Conservation laws and variational structure of damped nonlinear wave equations
论文作者
论文摘要
对于一级非线性波方程，都发现了所有低阶保护定律，并具有线性阻尼，这是允许时间依赖的。这种方程在众多的物理应用中出现，并且在分析中引起了很多关注。保护定律描述了普遍的动量和增强动量，保形动量，广义能量，扩张能和轻锥能量。保形动量和扩张能在一个维度上没有针对非线性未阻尼波方程的对应物。所有保护定律都是可以通过Noether定理获得的，这是适用的，因为阻尼项可以通过更改因变量的变化转化为依赖时间依赖的自我相互作用项。对于几种保护定律，相应的变分对称性具有一种新型形式，该形式与一维非线性未固定波方程所接受的任何众所周知的变异对称性不同。
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted much attention in analysis. The conservation laws describe generalized momentum and boost momentum, conformal momentum, generalized energy, dilational energy, and light-cone energies. Both the conformal momentum and dilational energy have no counterparts for nonlinear undamped wave equations in one dimension. All of the conservation laws are obtainable through Noether's theorem, which is applicable because the damping term can be transformed into a time-dependent self-interaction term by a change of dependent variable. For several of the conservation laws, the corresponding variational symmetries have a novel form which is different than any of the well known variation symmetries admitted by nonlinear undamped wave equations in one dimension.
