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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Solitons and Breathers in the modulus KdV equations
模量 KdV方程 孤子 呼吸器
2023/5/12
Compared to the soliton solutions, the breathers, which are constructed in the mKdV or Gardner equation via integrability methods, are less studied. In our numerical study, we show the interactions be...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Low regularity conservation laws for the fifth-order modified KdV equations in Besov spaces
Besov空间 五阶修正KdV方程 低正则性 守恒定律
2023/4/19
We get a priori estimates for the fifth-order modified KdV equations in Besov spaces with low regularity which cover the full subcritical range. These estimates are obtained from the power series expa...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：与Lamé函数相关的tau函数与顶点算子: KdV
Lamé函数 tau函数 顶点算子 KdV
2023/5/5
Lamé函数可以视为当势函数取Weierstrass的p函数时Schr?dinger谱问题的解。KdV/KP型的可积系统存在以Lamé函数为平面波因子的精确解。报告将以KdV方程为例，介绍基于Lamé函数的双线性方法框架，包括：椭圆色散关系、双线性方程的拟规范性质、tau函数、顶点算子的椭圆形变、双线性等式。
Dissipative behavior of some fully non-linear KdV-type equations
KdV-type equations Finite-difference methods Nonlinear dynamics
2015/10/8
The KdV equation can be considered as a special case of the general equationutCf .u/x−g.uxx/x D 0;> 0;wheref is
non-linear andg is linear, namelyf .u/ D u2=2 andg.v/ D v. As the parameter t...
Well-posedness for the fifth-order KdV equation in the energy space
Fifth-order KdV equation fifth-order water-waves models initial value problem
2012/5/9
We prove that the initial value problem (IVP) associated to the fifth order KdV equation {equation} \label{05KdV} \partial_tu-\alpha\partial^5_x u=c_1\partial_xu\partial_x^2u+c_2\partial_x(u\partial_x...
CK Method And Auto-Backlund Transformation To Find New Exact Solutions Of The (1+1)-Dimensional Variable-Coefficient KdV Equation
CK Method auto-B¨acklund transformation soliton-type solutions
2011/10/18
In this letter, based on the computerized symbolic computation, we extend the Clarkson and Kruskal (CK) method to search for new soliton-type solutions and auto-B¨acklund transformation of partial dif...
KdV equation in the quarter--plane: evolution of the Weyl functions and unbounded solutions
KdV initial–boundary value problem Weyl function evolution low–energy asymptotics blow–up solution
2011/9/1
Abstract: The matrix KdV equation with a negative dispersion term is considered in the right upper quarter--plane. The evolution law is derived for the Weyl function of a corresponding auxiliary linea...
Semiclassical limit for generalized KdV equations before the gradient catastrophe
Semiclassical limit generalized KdV equations the gradient catastrophe Analysis of PDEs
2011/8/24
Abstract: We study the semiclassical limit of the (generalised) KdV equation, for initial data with Sobolev regularity, before the time of the gradient catastrophe of the limit conservation law. In pa...
Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation
the first Painlevé hierarchy non-generic critical behavior the KdV equation
2011/8/23
Abstract: We establish the existence of real pole-free solutions to all even members of the Painlev\'e I hierarchy. We also obtain asymptotics for those solutions and describe their relevance in the d...
借助Lie群研究Burgers-KdV方程行波解的可积性
Burgers-KdV行波解方程 Lie群 首次积分
2013/10/20
运用经典Lie群方法证明 Burgers-KdV 方程行波解所满足的二阶非线性常微分方程当且仅当参数满足特殊情况下,恰好接受一个两参数Lie群, 并用不同的方法求出方程的两个相互独立首次积分.
Conserved quantities and generalized solutions of the ultradiscrete KdV equation
Conserved quantities generalized solutions ultradiscrete KdV equation
2011/2/22
We construct generalized solutions to the ultradiscrete KdV equation,including the so-called negative solition solutions. The method is based on the ultradiscretization of soliton solutions to the dis...
The linear stability of traveling waves to the compound Kdv-Burgers equation
compound Kdv-Burgers equation inear stability
2010/9/21
Herein the traveling waves of compound Kdv-Burgers are considered,.with the help of an analytic function D(λ), the traveling wave is stable.
Variational iteration method for solving coupled Schrodinger-KdV equation
Variational iteration method (VIM) the coupled Schrö dinger–KdV equation
2010/9/21
In this letter, we will consider variational iteration method (VIM) for finding analytical solutions of the coupled Schrödinger–KdV equation. The available analytical solutions of the coupled Sch...
The Hirota τ-function and well-posedness of the KdV equation with an arbitrary step like initial profile decaying on the right half line
Korteweg-de Vries equation inverse scattering transform Schr ¨odinger operator
2011/3/1
We are concerned with the Cauchy problem for the KdV equation on the whole line with an initial profile V0 which is decaying sufficiently fast at +¥ and arbitrarily enough (i.e., no decay or patte...
We consider the Cauchy problem of the fifth order KdV equation with low regularity initial data. We cannot apply the iteration argument to this problem when initial data is given in the Sobolev space...