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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...
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 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
2010/12/28
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...