论文标题
非线性声学中Westervelt方程的对称分析和隐藏的变分结构
Symmetry analysis and hidden variational structure of Westervelt's equation in nonlinear acoustics
论文作者
论文摘要
Westervelt的方程是一种非线性波方程，可广泛用于模拟可压缩介质中声波的传播，其中一种重要的应用是在人体组织中超声波检查。现代方法研究了该方程式的两个基本方面 - 对称和保护法。获得了许多结果：新的保守积分；潜在的系统产生隐藏的对称性和非局部保护定律；在未阻尼的情况下，将Westervelt方程映射到线性波方程中；映射产生的确切解决方案；隐藏的差异结构，包括拉格朗日和哈密顿族人；递归操作员和固定运营商；接触对称性；高阶符号和保护法。
Westervelt's equation is a nonlinear wave equation that is widely used to model the propagation of sound waves in a compressible medium, with one important application being ultra-sound in human tissue. Two fundamental aspects of this equation -- symmetries and conservation laws -- are studied in the present work by modern methods. Numerous results are obtained: new conserved integrals; potential systems yielding hidden symmetries and nonlocal conservation laws; mapping of Westervelt's equation in the undamped case into a linear wave equation; exact solutions arising from the mapping; hidden variational structures, including a Lagrangian and a Hamiltonian; a recursion operator and a Noether operator; contact symmetries; higher-order symmetries and conservation laws.
