Mathematical Sciences: Non-classical symmetries of differential equations

在传统的分组方法之外发展新的方法- 不变量解，用于求系统的显式解 偏微分方程，并将其应用于物理 重要系统和边值问题。 该方法的 研究将包括非经典对称性，部分 不变解，部分对称，Clarkson-Kruskal 直接法和弱对称群。 这些方法都可以 通过“边条件”的一般理论被包含， 超定偏微分方程组 的 该项目的重点将是确定新的 重要物理边值问题的精确解 偏微分方程的混合问题。

To develop new methods beyond the classical method of group- invariant solutions for finding explicit solutions to systems of partial differential equations, and apply them to physically important systems and boundary value problems. The methods to be investigated will include non-classical symmetries, partially invariant solutions, partial symmetries, the Clarkson-Kruskal direct method, and weak symmetry groups. These methods can all be subsumed through the general theory of "side conditions" and overdetermined systems of partial differential equations. The emphasis of this project will be on the determination of new exact solutions to physically important boundary value, Cauchy and mixed problems for partial differential equations.