论文标题
AKNS层次结构负部分的第一个成员的矢量二进制Darboux转换
A vectorial binary Darboux transformation of the first member of the negative part of the AKNS hierarchy
论文作者
论文摘要
使用BidiverentialCiculus，我们为AKNS层次结构的“负”部分的第一个成员得出了矢量二进制Darboux变换。还原导致NLS层次结构的第一个“负流”，这又是二维中相当简单的非线性复合物PDE的降低，并带有领先的混合第三衍生物。该PDE可以被认为是描述一个维度在一个维的复杂标量场的几何动力学，因为它在两个自变量之一的坐标转换下是不变的。我们利用相应降低的矢量二进制darboux变换来生成PDE的多氧化解决方案，还具有对自变量和平面波背景的额外理性依赖性。这包括流氓波。
Using bidifferential calculus, we derive a vectorial binary Darboux transformation for the first member of the "negative" part of the AKNS hierarchy. A reduction leads to the first "negative flow" of the NLS hierarchy, which in turn is a reduction of a rather simple nonlinear complex PDE in two dimensions, with a leading mixed third derivative. This PDE may be regarded as describing geometric dynamics of a complex scalar field in one dimension, since it is invariant under coordinate transformations in one of the two independent variables. We exploit the correspondingly reduced vectorial binary Darboux transformation to generate multi-soliton solutions of the PDE, also with additional rational dependence on the independent variables, and on a plane wave background. This includes rogue waves.
