An efficient and accurate numerical scheme is proposed, analyzed and implemented for the Kawahara and modified Kawahara equations which model many physical phenomena such as gravity-capillary waves and magneto-sound propagation in plasmas. The scheme consists of dual-Petrov-Galerkin method in space and Crank-Nicholson-leap-frog in time such that at each time step only a sparse banded linear sys...

In this paper, we consider the Kawahara equation in a bounded interval and with delay term one of boundary conditions. Using two different approaches, prove that system is exponentially stable under condition on length spatial domain. Specifically, first result obtained by introducing suitable energy functional using Lyapunov’s approach, to ensure goes 0 as $$t \rightarrow \infty $$ . The secon...

In this study, we establish exact solutions of fractional Kawahara equation by using the idea of [Formula: see text]-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, t...

Near-wall turbulence in the buffer region is qualitatively characterized in terms of recentlyfound nonlinear three-dimensional solutions to the incompressible Navier–Stokes equation for wall-bounded shear flows. Jiménez & Simens’ (2001) traveling-wave solution for an autonomous wall flow, Nagata’s (1990) steady and Kawahara & Kida’s (2001) periodic solutions for a plane Couette flow are conside...

We develop a robust Christov–Galerkin spectral technique for computing interacting localized wave solutions of and fourth and sixth-order generalized wave equations. To this end, a special complete orthonormal system of functions in Lð 1;1Þ is used whose rate of convergence is shown to be exponential for the cases under consideration. For the time-stepping, an implicit algorithm is chosen which...