A type of nonlinearity in vibrational engineering systems emerges when the restoring force is a nonlinear function of displacement. The derivative of this function is known as stiffness. If the stiffness increases by increasing the value of displacement from the equilibrium position, then the system is known as hardening type oscillator and if the stiffness decreases by increasing the value of ...

We consider the periodic initial value problem for the Kuramoto–Sivashinsky (KS) equation. We approximate the solution by discretizing in time by implicit–explicit BDF schemes and in space by a pseudo–spectral method. We present the results of various numerical experiments.

the construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. we apply this system as basis functions to solve the fractional differential and integro-differential equations. biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. some test pr...

After extending the Clarkson-Kruskal’s direct similarity reduction ansatz to a more general form, one may obtain various new types of reduction equations. Especially, some lower dimensional turbulence systems or chaotic systems may be obtained from the general type of similarity reductions of a higher dimensional Lax integrable model with nonintegrable boundary and/or the initial conditions. In...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 1 October 2020Accepted: 02 July 2021Published online: 28 2021KeywordsKuramoto--Sivashinsky, coordinate-free model flame front, well-posedness, asymptotic behaviorAMS Subject Headings35B40, 35B65Publication DataISSN (online): 1536-0040Publisher: Society for Industrial and ...

Abstract Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence chaos, rigorous computation these is certainly possible, but mathematically complicated computationally expensive. Based on Ruelle’s formalism, this paper shows that sophisticated linear response algorithm can be dramatically simplified h...

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.