A new composite Runge–Kutta (RK) method is proposed for semilinear partial differential equations such as Korteweg–de Vries, nonlinear Schrödinger, Kadomtsev– Petviashvili (KP), Kuramoto–Sivashinsky (KS), Cahn–Hilliard, and others having high-order derivatives in the linear term. The method uses Fourier collocation and the classical fourth-order RK method, except for the stiff linear modes, whi...

We consider the stochastic non-autonomous Kuramoto-Sivashinsky equation with multiplicative white noise and colored coefficients. Due to anti-dissipative term in equation, we restrict state space on Lebesgue of odd functions then obtain a pullback random attractor $ \mathcal{A} space, where special bridge function plays an crucial role priori estimate. Moreover, prove continuity expectation for...

in this paper we obtain  exact solutions of the generalized kuramoto-sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems.    the methods used  to determine the exact solutions of the underlying equation are the lie group analysis  and the simplest equation method. the solutions obtained are  then plotted.

In this article, a nonic B-spline collocation approach is applied to solve the approximate solution of Kuramoto-Sivashinsky equation (KSE). Here nonlinear term KSE linearizing using Taylo...

We develop an algorithm based on the nudging data assimilation scheme for concurrent (on-the-fly) estimation of scalar parameters a system evolutionary dissipative partial differential equations in which state is partially observed. The takes advantage error that results from with incorrect true system. intuitive nature makes its extension to several different systems immediate, and it allows r...

The work proposes and studies a model for one-dimensional spatially extended systems, which involve nonlocal interactions and finite propagation speed. It shows that the general reaction-diffusion equation, the Swift-Hohenberg equation, and the general Kuramoto-Sivashinsky equation represent special cases of the proposed model for limited spatial interaction ranges and for infinite propagation ...

In this article, we investigate the nonlinear model describing various physical and chemical phenomena named Kuramoto–Sivashinsky equation. We implemented natural decomposition method, a novel technique, mixed with Caputo–Fabrizio (CF) Atangana–Baleanu deriavatives in Caputo manner (ABC) fractional derivatives for obtaining approximate analytical solution of equation (FKS). The proposed method ...