AKNS族负部分第一成员的向量二元达布变换
A vectorial binary Darboux transformation of the first member of the negative part of the AKNS hierarchy
摘要：
使用双微分，我们推导出一个矢量二进制达布变换的第一个成员的“负”的AKNS层次的一部分。一个减少导致第一个“负流”的NLS层次，这反过来又是一个减少一个相当简单的非线性复杂的偏微分方程在两个维度上，与领先的混合三阶导数。这个偏微分方程可以被看作是描述一个复杂的标量场在一维的几何动力学，因为它是在坐标变换下的两个独立变量之一不变。我们利用相应的减少矢量二进制达布变换生成多孤子解的PDE，也有额外的合理依赖的独立变量，并在平面波背景。这包括流氓波。
英文摘要：
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.
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