Modified Kuramoto-Sivashinsky equation: Stability of stationary solutions and the consequent dynamics
نویسندگان
چکیده
منابع مشابه
Modified Kuramoto-Sivashinsky equation: stability of stationary solutions and the consequent dynamics.
We study the effect of a higher-order nonlinearity in the standard Kuramoto-Sivashinsky equation: partial differentialxG(Hx). We find that the stability of steady states depends on dv/dq , the derivative of the interface velocity on the wave vector q of the steady state. If the standard nonlinearity vanishes, coarsening is possible, in principle, only if G is an odd function of Hx. In this case...
متن کاملExact Solutions of the Generalized Kuramoto-Sivashinsky Equation
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.
متن کاملComputational Study of the Dispersively Modified Kuramoto-Sivashinsky Equation
We analyze and implement fully discrete schemes for periodic initial value problems for a general class of dispersively modified Kuramoto–Sivashinsky equations. Time discretizations are constructed using linearly implicit schemes and spectral methods are used for the spatial discretization. The general case analyzed covers several physical applications arising in multi-phase hydrodynamics and t...
متن کاملexact solutions of the generalized kuramoto-sivashinsky equation
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.
متن کاملMeromorphic traveling wave solutions of the Kuramoto–Sivashinsky equation
We determine all cases when there exists a meromorphic solution of the ODE νw + bw + μw + w/2 +A = 0. This equation describes traveling waves solutions of the KuramotoSivashinsky equation. It turns out that there are no other meromorphic solutions besides those explicit solutions found by Kuramoto and Kudryashov. The general method used in this paper, based on Nevanlinna theory, is applicable t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 2007
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.75.027202