论文标题
偏微分方程的伴随隔离的几何配方
Geometrical formulation for adjoint-symmetries of partial differential equations
论文作者
论文摘要
研究了对伴随隔离的几何公式作为1形式的一般偏微分方程（PDE），该方程提供了对称性的几何含义的双重对应，作为PDE的解决方案空间上的切线矢量场。提出了此配方的两种应用。此外，对于进化方程的系统，显示伴随对称具有另一种由1形式给出的几何公式，这些配方在系统在解决方案空间上产生的流量下是不变的。该结果概括为具有空间约束的演化方程系统，其中显示出与约束方程相关的正常1形式的功能乘数显示出不变的1形式。所有结果都适用于应用数学和数学物理学的PDE系统。
A geometrical formulation for adjoint-symmetries as 1-forms is studied for general partial differential equations (PDEs), which provides a dual counterpart of the geometrical meaning of symmetries as tangent vector fields on the solution space of a PDE. Two applications of this formulation are presented. Additionally, for systems of evolution equations, adjoint-symmetries are shown to have another geometrical formulation given by 1-forms that are invariant under the flow generated by the system on the solution space. This result is generalized to systems of evolution equations with spatial constraints, where adjoint-symmetry 1-forms are shown to be invariant up to a functional multiplier of a normal 1-form associated to the constraint equations. All of the results are applicable to the PDE systems of interest in applied mathematics and mathematical physics.
