论文标题
二维耦合非线性schrödinger方程的无限尺寸对称代数的有限尺寸子代数分类
The finite dimensional subalgebra classification of infinite dimensional symmetry algebra of two dimensional coupled nonlinear Schrödinger equations
论文作者
论文摘要
考虑了二维耦合非线性shrödinger方程的对称组结构。我们首先表明该方程允许无限的尺寸对称代数以及相应的对称组取决于一个变量的四个任意函数。然后，我们显示一些物理对称性和方程对称代数中包含的仿射环代数。第三，我们给出了对称组的对称代数的有限维度（少于四个）的子代数的完整分类。这些结果为通过对称方法进一步研究方程提供了理论和计算基础。
The symmetry group structures of two dimensional coupled nonlinear Shrödinger equations are considered. We first show that the equations admit infinite dimensional symmetry algebra as well as the corresponding symmetry group depending on four arbitrary functions of one variable. Then we show some physical symmetries and an affine loop algebra contained in the symmetry algebra of the equations. Third, we give the complete classifications of finite dimension (less than four) subalgebras of the symmetry algebra under the adjoint group of the symmetry group. These results provide the theoretical and computational basis for the further study of the equations with symmetry methods.
