Mathematical Sciences: Non-classical symmetries of differential equations

开发新的方法，超越经典的群不变解的方法来求偏微分方程组的显式解，并将其应用于物理上重要的系统和边值问题。要研究的方法将包括非经典对称，部分不变解，部分对称，克拉克森-克鲁斯卡尔直接方法和弱对称群。这些方法都可以通过“边条件”和偏微分方程的过定系统的一般理论纳入。这个项目的重点将是确定新的精确解的物理上重要的边值，柯西和混合问题的偏微分方程。

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.