（3+1）维短波方程的不变子空间和精确解

摘要

利用不变子空间方法研究了(3+1)维短波方程的不变子空间和精确解。在(2+1)维短波方程增加一维的情形下，构造了更加广泛的精确解，同时也得到了超曲面的爆破解。主要结果不仅推广了不变子空间理论在高维非线性偏微分方程中的应用，而且对研究高维方程的动力系统有重要意义。%Considered herein is invariant spaces and exact solutions of (3+1) dimensional short wave equation with the invariant spaces method. More exact solution and hyperspace blow-up solution are obtained in case of increasing one dimension for (2+1) dimensional short wave equation. The results not only extend the application of the theory of invariant subspace in high-dimensional nonlinear partial differential equations, but also have a great meaning for study high-dimensional dynamical system equations.