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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Long-time asymptotics of soliton equations via the nonlinear steepest descent method
非线性 最速下降法 孤立子方程 长时间渐近性
2023/11/13
Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed in order to study the asymptotic analysis of solutions of some nonlinear evolution equations associat...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach: Part I continuous case
KP-户田约简法 NLS类型 方程孤子解 统一方法 离散情况
2023/4/27
In these two talks, I will present a unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach. I will take the NLS equation as a typical example and show h...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Defocusing NLS equation with nonzero background: Soliton resolution in soliton region
非零背景 散焦NLS方程 孤子区域 孤子分辨率
2023/5/5
Consider to the Cauchy problem of the defocusing NLS equation with a nonzero background. With the Dbar generalization of the nonlinear steepest descent method to compute the leading order approximatio...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Bilinear approaches in soliton theory II: N-soliton solutions in (2+1)-dimensions
孤子理论 双线性方法 （2+1）维 N-孤子解
2023/5/6
The talk is about applications of bilinear approaches to N-soliton solutions in (2+1)-dimensions. The Hirota N-soliton condition will be analyzed, together with novel examples of (2+1)-dimensional sol...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Bilinear approaches in soliton theory I: Hirota direct method and its applications in (1+1)-dimensions
孤子理论 双线性方法 广田直接法 （1+1）维
2023/5/6
We will talk about the Hirota direct method and its applications to soliton solutions in (1+1)-dimensions. Both known and new examples of soliton equations will be discussed, and generalized bilinear ...