论文标题
对称动作和伴随伴随的括号。 II：实例
Symmetry actions and brackets for adjoint-symmetries. II: Physical examples
论文作者
论文摘要
对称性和伴随对称是PDE系统的两个基本（无坐标）结构。最近的工作已经开发了伴随分节的几个新代数方面：对称性对伴随的三种基本作用；在对称作用范围内给出的伴随对称的集合；由任何非变化的伴随对称性构建的概括性（前隔离）算子。此处通过考虑了五个物理上有趣的非线性PDE系统的示例 - 非线性反应扩散方程，可压缩粘性流体流动，表面重力水波方程，耦合单位波方程和非线性声音方程。
Symmetries and adjoint-symmetries are two fundamental (coordinate-free) structures of PDE systems. Recent work has developed several new algebraic aspects of adjoint-symmetries: three fundamental actions of symmetries on adjoint-symmetries; a Lie bracket on the set of adjoint-symmetries given by the range of a symmetry action; a generalized Noether (pre-symplectic) operator constructed from any non-variational adjoint-symmetry. These results are illustrated here by considering five examples of physically interesting nonlinear PDE systems -- nonlinear reaction-diffusion equations, Navier-Stokes equations for compressible viscous fluid flow, surface-gravity water wave equations, coupled solitary wave equations, and a nonlinear acoustic equation.
