We analyze coherent structures in nonlocal dispersive active-dissipative nonlinear systems, using as a prototype the Kuramoto–Sivashinsky (KS) equation with an additional nonlocal term that contains stabilizing/destabilizing and dispersive parts. As for the local generalized Kuramoto–Sivashinsky (gKS) equation (see, e.g., [T. Kawahara and S. Toh, Phys. Fluids, 31 (1988), pp. 2103–2111]), we sho...

We report the observation of defects with fractional topological charges (disclinations) in square and hexagonal patterns as numerical solutions of several generic equations describing many pattern-forming systems: Swift-Hohenberg equation, damped Kuramoto-Sivashinsky equation, as well as nonlinear evolution equations describing large-scale Rayleigh-Benard and Marangoni convection in systems wi...

The damped Kuramoto-Sivashinsky equation has emerged as a fundamental tool for the understanding of the onset and evolution of secondary instabilities in a wide range of physical phenomena. Most existing studies about this equation deal with its asymptotic states on one-dimensional settings or on periodic square domains. We utilize a large-scale numerical simulation to investigate the asymptoti...

On the example of a nite dimensional approximation of the Kuramoto-Sivashinsky equation we show how topological methods may be successfully used in computer assisted proofs of the existence of heteroclinic connections in ordinary diierential equations.

A non-isotropic version of phase equations such as the Burgers equation, the K-dV-Burgers equation, the Kuramoto-Sivashinsky equation and the Benney equation in the three-dimensional space is systematically derived from a general reaction-diffusion system by means of the renormalization group method. PACS codes: 47.20.Ky

we show how daubechies wavelets are used to solve kuramoto-sivashinsky type equations with periodic boundary condition‎. ‎wavelet bases are used for numerical solution of the kuramoto-sivashinsky type equations by galerkin method‎. ‎the numerical results in comparison with the exact solution prove the efficiency and accuracy of our method‎.

<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...

Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online's data policy on reuse of materials please consult the policies page. We study the emergence of pattern formation and chaotic dynamics in the one-dimensional (1D) generalized Kuramoto-Sivashinsky (gKS) equation by means of a ...