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Global well-posedness for the Kawahara equation with low regularity data
Kawahara equation global well-posedness Cauchy problem I-method
2012/3/1
We consider the global well-posedness for the Cauchy probelem of the Kawahara equation which is one of the fifth order KdV type equations. We first establish the local well-posedness in a more suitabl...
Comment on：“New exact solutions for the Kawahara equation using Exp-function method”
Nonlinear evolution equation Kawahara equation Exactso-lution Exp-function method
2010/4/21
Exact solutions of the Kawahara equation by Assas [L.M.B. Assas, J. Com. Appl. Math. 233 (2009) 97--102] are analyzed. It is shown that all solutions do not satisfy the Kawahara equation and conseque...
Exact and numerical solution of Kawahara equation by the variational iteration method
Variational iteration method Kawahara equation
2010/9/14
In this Letter, exact and numerical solutions are obtained for the Kawahara equation by the known variational iteration method (VIM). This method is based on Lagrange multipliers for identification of...
Global Existence of Solutions for the Cauahy Problem of the Kawahara Equation with $L^2$ Initial Data
Kawahara equation Cauchy problem global solution
2007/12/11
In this paper we study solvability of the Cauchy problem of the Kawahara equation $\partial_tu+au\partial_xu+\beta\partial^3_xu+\gamma\partial^5_xu =0$ with $L^2$ initial data. By working on the Bourg...
Global Existence of Solutions for the Kawahara Equation in Sobolev Spaces of Negative Indices
Kawahara equation Cauchy problem global solution almost conservation law
2007/12/11
We first prove that the Cauchy problem of the Kawahara equation, $\partial_tu+u\partial_xu+\beta\partial_x^3u+\gamma\partial_x^5u=0,$ is locally solvable if the initial data belong to $H^{r}(\bf{R})...