论文标题
在具有时间依赖边界条件的非线性schrödinger方程
On the nonlinear Schrödinger equation with a time-dependent boundary condition
论文作者
论文摘要
我们在半线上研究了涉及时间导数的边界条件的非线性schrödinger方程。 Zambon提出了这种边界条件[J.高能量。物理。 2014（2014）36]。我们通过使用Sklyanin的形式主义以及使用Bäcklund变换的工具以及适当的反射类型来建立这种边界的整合性。此外，我们提出了一种通过Darboux转换方法与边界敷料技术结合使用的Darboux转换方法来推导边界问题多索氏溶液的明确公式的方法。
We study the nonlinear Schrödinger equation on the half-line with a boundary condition that involves time derivative. This boundary condition was presented by Zambon [J. High Energ. Phys. 2014 (2014) 36]. We establish the integrability of such a boundary both by using the Sklyanin's formalism and by using the tool of Bäcklund transformations together with a suitable reduction of reflection type. Moreover, we present a method to derive explicit formulae for multi-soliton solutions of the boundary problem by virtue of the Darboux transformation method in conjunction with a boundary dressing technique.
