标题： 带非平凡种子的GBDT：聚焦NLS方程的显式解及其对应的Weyl函数 显示英文标题

标题： GBDT with nontrivial seeds: explicit solutions of the focusing NLS equations and the corresponding Weyl functions

摘要： 我们的广义Bäcklund-Darboux变换（GBDT）方法用于构造聚焦非线性薛定谔（NLS）方程在指数种子 $a \exp\{2 i (cx +dt)\}$ 情况下的显式解。同时获得了对应的Baker-Akhiezer函数以及Weyl函数的演化。 特别是，考虑了出现在NLS方程的 rogue 波、阶跃型解和 $N$ 调制解的研究中的解。 这项工作是我们与Rien Kaashoek和Israel Gohberg合作工作的实质性发展，其中种子是平凡的，也是我们之前几项工作的延续。 显示英文摘要

摘要： Our GBDT (generalised B\"acklund-Darboux transformation) approach is used to construct explicit solutions of the focusing nonlinear Schr\"odinger (NLS) equation in the case of the exponential seed $a \exp\{2 i (cx +dt)\}$. The corresponding Baker-Akhiezer functions and evolution of the Weyl functions are obtained as well. In particular, the solutions, which appear in the study of rogue waves, step-like solutions and $N$-modulation solutions of the NLS equation are considered. This work is an essential development of our joint work with Rien Kaashoek and Israel Gohberg, where the seed was trivial, as well as several other of our previous works.