A nonlinear Liouville property for the generalized Kawahara equation

Soliton Perturbation Theory for the Generalized Kawahara Equation

Department of Physics and Pre-Engineering Center for Research and Education in Optical Sciences and Applications Delaware State University, Dover, DE 19901-2277, USA Abstract The adiabatic parameter dynamics of solitons, due to the generalized Kawahara equation are obtained in this paper. The soliton perturbation theory is exploited to obtain the results. Also, the change in the velocity is obt...

Computable Analysis of the Solution of the Nonlinear Kawahara Equation

In this paper, we study the computability of the solution operator of the initial problem for the nonlinear Kawahara equation, which is based on the Type-2 Turing machines. We will prove that in Sobolev space 2 ( ) s H R , for 0 s ≥ , the solution operator: 2 : ( ) s R K H R → ( ; C R 2 ( )) s H R is ( ,[ s H δ ρ → ]) s H δ -computable. The conclusion enriches the theory of computability. Key w...

The Kawahara equation in weighted Sobolev spaces

Abstract The initialand boundary-value problem for the Kawahara equation, a fifthorder KdV type equation, is studied in weighted Sobolev spaces. This functional framework is based on the dual-Petrov–Galerkin algorithm, a numerical method proposed by Shen (2003 SIAM J. Numer. Anal. 41 1595–619) to solve third and higher odd-order partial differential equations. The theory presented here includes...

Unique continuation property for a higher order nonlinear Schrödinger equation

We prove that, if a sufficiently smooth solution u to the initial value problem associated with the equation ∂t u+ iα∂2 xu+ β∂3 xu+ iγ |u|2u+ δ|u|∂xu+ u∂xu= 0, x, t ∈R, is supported in a half line at two different instants of time then u≡ 0. To prove this result we derive a new Carleman type estimate by extending the method introduced by Kenig et al. in [Ann. Inst. H. Poincaré Anal. Non Linéair...

Using multiquadric quasi-interpolation for solving Kawahara equation