we introduce a new solution for kawahara-kdv equations. the lie group analysis is used to carry out the integration of this equations. the similarity reductions and exact solutions are obtained based on the optimal system method.

We study the stability of spatially periodic solutions to the Kawahara equation, a fifth order, nonlinear partial differential equation. The equation models the propagation of nonlinear water-waves in the long-wavelength regime, for Weber numbers close to 1/3 where the approximate description through the Korteweg-de Vries (KdV) equation breaks down. Beyond threshold, Weber number larger than 1/...

<p style='text-indent:20px;'>In this paper, we are concerned with the existence of solitary waves for a generalized Kawahara equation, which is model equation describing solitary-wave propagation in media. We obtain some qualitative properties equilibrium points and results wave solutions without delay perturbation by employing phase space analysis. Furthermore two types special convoluti...