This work is devoted to present Massera-type theorems for the Kawahara system, a higher order dispersive equation, posed in bounded domain. Precisely, thanks some properties of semigroup and decays solutions this we are able prove its periodic, quasi-periodic almost periodic.

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...

In the first part of this work we study local well-posedness dispersive equations in weighted spaces $$H^s({\mathbb {R}})\cap L^2(|x|^{2b}dx)$$ . We then apply our results for several models such as Hirota-Satsuma system, OST equation, Kawahara equation and a fifth-order model. Using these results, second is devoted to obtain related blow up system.

Variational iteration method and homotopy perturbation method are introduced to solve the Kawahara equation. Comparison of the obtained results with the numerical solution shows that both methods lead to remarkably accurate solutions. The main property of the both methods is its flexibility and ability to solve nonlinear equations accurately and conveniently.