Nonclassical Symmetries for Nonlinear Partial Differential Equations via Compatibility

• 来源期刊: 理论物理通讯：英文版
• 学科: 工学
• 关键词: 非线性偏微分方程 非经典 对称性 Boussinesq方程 相容性 浅水波方程 确定方程 表面条件
• 年，卷（期）: 2011,（10）
• 页码范围: 611-616
• 页数: 6页
• 分类号: O175.29|TN241
• 语种: 英文

摘要

The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The （2＋1）-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples i11ustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries.