On Damping Rates of dissipative KdV equations

نویسندگان

  • Jean-Paul Chehab
  • Georges Sadaka
چکیده

We consider here different models of dissipative Korteweg-de Vries (KdV) equations on the torus. Using a proper wave function Γ, we compare numerically the long time behavior effects of the damping models and we propose a hierarchy between these models. We also introduce a method based on the solution of an inverse problem to rebuild a posteriori the damping operator using only samples of the solution.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Damping of large-amplitude solitary waves

Soliton damping in weakly dissipative media has been studied for several decades, usually using the asymptotic theory of the slowly-varying solitary wave solution of the Korteweg-de Vries (KdV) equation. Damping then occurs according to the energy balance equation, and a shelf is generated behind the soliton. Various examples of this process have been given by Ott & Sudan (1970) Pelinovsky (197...

متن کامل

Global Attractor for the Generalized Dissipative KDV Equation with Nonlinearity

In order to study the longtime behavior of a dissipative evolutionary equation, we generally aim to show that the dynamics of the equation is finite dimensional for long time. In fact, one possible way to express this fact is to prove that dynamical systems describing the evolutional equation comprise the existence of the global attractor 1 . The KDV equation without dissipative and forcing was...

متن کامل

Global well-posedness for dissipative Korteweg-de Vries equations

This paper is devoted to the well-posedness for dissipative KdV equations ut+uxxx+|Dx| u+uux = 0, 0 < α ≤ 1. An optimal bilinear estimate is obtained in Bourgain’s type spaces, which provides global wellposedness in Hs(R), s > −3/4 for α ≤ 1/2 and s > −3/(5−2α) for α > 1/2.

متن کامل

Long-time Asymptotic Behavior of Dissipative Boussinesq Systems

In this paper, we study various dissipative mechanics associated with the Boussinesq systems which model two-dimensional small amplitude long wavelength water waves. We will show that the decay rate for the damped one-directional model equations, such as the KdV and BBM equations, holds for some of the damped Boussinesq systems.

متن کامل

Lie symmetry analysis for Kawahara-KdV equations

We introduce a new solution for Kawahara-KdV equations. The Lie group analysis is used to carry out the integration of this equations. The similarity reductions and exact solutions are obtained based on the optimal system method.

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012