标题： 偏微分方程的不变约化。 II：一般机制 显示英文标题

标题： Invariant Reduction for Partial Differential Equations. II: The General Mechanism

摘要： 一种减少对称性不变守恒律、预辛结构和偏微分方程（PDEs）变分原理的机制被提出。 该机制适用于任何具有局部（点、接触或更高）对称性的PDE系统，并将对称性不变守恒律，以及预辛结构、变分原理等与描述相应不变解的系统的类似物联系起来。 提出了满足对称性不变解的PDE系统的诺特定理的一个版本。 考虑了几个详细的例子，包括点对称性和更高对称性不变的情况。 显示英文摘要

摘要： A mechanism of reduction of symmetry-invariant conservation laws, presymplectic structures, and variational principles of partial differential equations (PDEs) is proposed. The mechanism applies for an arbitrary PDE system that admits a local (point, contact, or higher) symmetry, and relates symmetry-invariant conservation laws, as well as presymplectic structures, variational principles, etc., to their analogs for systems that describe the corresponding invariant solutions. A version of Noether's theorem for the PDE system satisfied by symmetry-invariant solutions is presented. Several detailed examples, including cases of point and higher symmetry invariance, are considered.