Heteroclinic Connections in the Kuramoto-Sivashinsky Equation: a Computer Assisted Proof
نویسندگان
چکیده
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.
منابع مشابه
Attracting Fixed Points for the Kuramoto-Sivashinsky Equation: A Computer Assisted Proof
We present a computer assisted proof of the existence of several attracting fixed points for the Kuramoto–Sivashinsky equation ut = (u )x − uxx − νuxxxx, u(x, t) = u(x+ 2π, t), u(x, t) = −u(−x, t), where ν > 0. The method is general and can be applied to other dissipative PDEs.
متن کاملRigorous Numerics for Dissipative Partial Differential Equations II. Periodic Orbit for the Kuramoto-Sivashinsky PDE-A Computer-Assisted Proof
We present a method of self-consistent a-priori bounds, which allows to study rigorously dynamics of dissipative PDEs. As an application present a computer assisted proof of an existence of a periodic orbit for the Kuramoto-Sivashinsky equation ut = (u )x− uxx− νuxxxx, u(t, x) = u(t, x + 2π), u(t, x) = −u(t,−x),
متن کاملSteady State Bifurcations for the Kuramoto-sivashinsky Equation - a Computer Assisted Proof
We apply the method of self-consistent bounds to prove the existence of multiple steady state bifurcations for Kuramoto-Sivashinski PDE on the line with odd and periodic boundary conditions.
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 کاملViscous Shocks in the Destabilized Kuramoto-Sivashinsky Equation
We study stationary periodic solutions of the Kuramoto-Sivashinsky (KS) model for complex spatiotemporal dynamics in the presence of an additional linear destabilizing term. In particular, we show the phase space origins of the previously observed stationary “viscous shocks” and related solutions. These arise in a reversible four-dimensional dynamical system as perturbed heteroclinic connection...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Reliable Computing
دوره 3 شماره
صفحات -
تاریخ انتشار 1997