论文标题
非零边界条件的非线性schrödinger方程的DBAR调味料方法
Dbar dressing method to nonlinear Schrödinger equation with nonzero boundary conditions
论文作者
论文摘要
扩展了DBAR敷料方法以研究具有非零边界条件的非线性Schrödinger（NLS）方程的聚焦/散焦。考虑了一种特殊的复杂功能。该功能是在环形周围内的Meromormormorphic，其中心为0，并满足环内部的局部DBAR问题。该功能的理论扩展到具有非零边界条件的NLS方程的lax对。在此过程中，建立了NLS电位与DBAR问题解决方案之间的关系。引入了DBAR问题的一定分布，以获得Focus/DeDocing NLS方程和保护定律。特殊分布给出了具有非零边界条件的焦点/散热NLS方程的明确解。
The Dbar dressing method is extended to study the focusing/defocusing nonlinear Schrödinger (NLS) equation with nonzero boundary condition. A special type of complex function is considered. The function is meromorphic outside an annulus with center 0 and satisfies a local Dbar problem inside the annulus. The theory of such function is extended to construct the Lax pair of the NLS equation with nonzero boundary condition. In this procedure, the relation between the NLS potential and the solution of the Dbar problem is established. A certain distribution for the Dbar problem is introduced to obtain the focusing/defocusing NLS equation and the conservation laws. The explicit solutions of the focusing/defocusing NLS equation with nonzero boundary condition are given from special distributions.
