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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 II discrete 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 the second part, I will mainly focus on two semi-discrete models: Ablowitz-Ladik equation and fully discrete NLS equation. First, I will clarify the connection of these two discrete models with dis...
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：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...
Ultradiscrete Plücker Relation Specialized for Soliton Solutions
Ultradiscrete Plücker Relation Specialized Soliton Solutions
2010/12/28
We propose an ultradiscrete analogue of Pl¨ucker relation specialized for soliton solutions.
It is expressed by an ultradiscrete permanent which is obtained by ultradiscretizing the per-
manent, tha...
Smooth soliton solutions of a new integrable equation by Qiao
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics(math-ph) Analysis of PDEs(math.AP) Pattern Formation and Solitons(nlin.PS)
2010/11/10
We find a transformation which relates a new third-order integrable nonlinear evolution equation, introduced recently by Qiao, with the well-known modified Korteweg - de Vries equation. Then we use th...
On reductions of soliton solutions of multi-component NLS models and spinor Bose-Einstein condensates
multicomponent nonlinear Schrodinger equations symmetric BD.I-type symmetric spaces
2010/4/1
We consider a class of multicomponent nonlinear Schrodinger equations (MNLS) related to the symmetric BD.I-type symmetric spaces. As important particular case of these MNLS we obtain the Kulish-Sklyan...
Multi-component Generalizations of Four Integrable Differential-difference Equations: Soliton Solutions and Bilinear Backlund Transformations
Soliton Solutions Bilinear Backlund Transformations
2012/7/31
Bilinear approach is applied to derive integrable multi-component generalizations of the socalled 1+1 dimensional special Toda lattice, the Volterra lattice, a simple di甧rential-di甧rence equation foun...