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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...
Schrödinger Equation with a Cubic Nonlinearity Sech-Shaped Soliton Solutions
Soliton Schrö dinger Equation Cubic Nonlinearity
2013/1/30
We first analyze the sech-shaped soliton solutions, either spatial or temporal of the 1D-Schrödinger equation with a cubic nonlinearity. Afterwards, these solutions are generalized to the 2D-Schr...
Non-Lie Point Symmetry and Coherent Soliton Solutions of Nizhnik-Novikov-Veselov Equation
Lax pair symmetries symmetry group exact solution
2012/9/24
A new method is presented to find the finite symmetry groups of nonlinear physics systems. For the (2+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation, both the Lie point symmetry and the non-Lie...
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...
A constructive approach to the soliton solutions of integrable quadrilateral lattice equations
soliton solutions quadrilateral lattice equations
2010/4/7
Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the Backlund transformation, and ...
A Unified and Explicit Construction
of N-Soliton Solutions for the Nonlinear Schrödinger Equation
Schrö dinger equation N-fold Darboux transformation
N-soliton solutions
2007/8/15
2001Vol.36No.4pp.401-404DOI:
A Unified and Explicit Construction
of N-Soliton Solutions for the Nonlinear Schrödinger Equation
FAN En-Gui
Institute of Mathematics, ...
Explicit N-Fold Darboux Transformations and Soliton
Solutions for Nonlinear Derivative Schrödinger Equations
derivative nonlinear Schrö dinger equations Gerdjikov-Ivanov
equation N-fold Darboux transformation N-soliton solution
2007/8/15
2001Vol.35No.6pp.651-656DOI:
Explicit N-Fold Darboux Transformations and Soliton
Solutions for Nonlinear Derivative Schrödinger Equations
FAN En-Gui1,2
1 Institute...
Soliton Solutions in Three-Component Bose-Einstein Condensates
Bose-Einstein condensate soliton
2007/8/15
2007Vol.47No.6pp.1063-1066DOI:
Soliton Solutions in Three-Component Bose-Einstein Condensates
ZHANG Xiao-Fei,1,2 XIE Chong-Wei,1 and WANG Shi-En2
1 Department of Physics...
A Simple Method to Obtain Exact Soliton Solutions for a Nonlinear Equation in a Loss Fibre System
nonlinear optics fibre communication
2007/8/15
2002Vol.38No.5pp.615-616DOI:
A Simple Method to Obtain Exact Soliton Solutions for a Nonlinear Equation in a Loss Fibre System
YANG Xiao-Xue1 and WU Ying1,2
1 Department...
Demonstration of Dark Soliton Solutions Found by Inverse Scattering Transform
inverse scattering transform dark soliton solutions
Liouville theorem
2007/8/15
2006Vol.46No.2pp.244-248DOI:
Demonstration of Dark Soliton Solutions Found by Inverse Scattering Transform
LI Cun, YANG Bai-Feng, CAI Hao, and HUANG Nian-Ning
Department...
New Soliton Solutions with Compact Support for a Family of
Two-Parameter Regularized Long-Wave Boussinesq Equations
nonlinear evolution equation R(m n) equations compacton solution
2007/8/15
2002Vol.37No.6pp.641-644DOI:
New Soliton Solutions with Compact Support for a Family of
Two-Parameter Regularized Long-Wave Boussinesq Equations
YAN Zhen-Ya
Department o...