Dissipationless hydrodynamics regularized by dispersion describe a number of physical media including water waves, nonlinear optics, and Bose–Einstein condensates. As in the classical theory of hyperbolic equations where a nonconvex flux leads to nonclassical solution structures, a nonconvex linear dispersion relation provides an intriguing dispersive hydrodynamic analogue. Here, the fifth orde...

The variational iteration method [1, 2], which is a modified general Lagrange multiplier method, has been shown to solve effectively, easily, and accurately a large class of nonlinear problems with approximations which converges (locally) to accurate solutions (if certain Lipschitz-continuity conditions are met). It was successfully applied to autonomous ordinary differential equations and nonl...

Abstract. One of the newest analytical methods to solve nonlinear dispersive wave equations is using both homotopy and perturbation methods which is called (HPM). Other the reliable methods are variational iteration method (VIM) by He and Adomian's decomposition method (ADM). Here, we compare the exact solution of HPM which are applied to solve a various fifth-order Korteweg-de Vries problems w...

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.

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equa...