Long-time Asymptotics for the Camassa-Holm Equation
نویسندگان
چکیده
We apply the method of nonlinear steepest descent to compute the longtime asymptotics of the Camassa–Holm equation for decaying initial data, completing previous results by A. Boutet de Monvel and D. Shepelsky.
منابع مشابه
On Time Fractional Modifed Camassa-Holm and Degasperis-Procesi Equations by Using the Haar Wavelet Iteration Method
The Haar wavelet collocation with iteration technique is applied for solving a class of time-fractional physical equations. The approximate solutions obtained by two dimensional Haar wavelet with iteration technique are compared with those obtained by analytical methods such as Adomian decomposition method (ADM) and variational iteration method (VIM). The results show that the present scheme is...
متن کاملA Coupling Problem for Entire Functions and Its Application to the Long-time Asymptotics of Integrable Wave Equations
We propose a novel technique for analyzing the long-time asymptotics of integrable wave equations in the case where the underlying isospectral problem has purely discrete spectrum. To this end we introduce a natural coupling problem for entire functions which serves as a replacement for the usual Riemann–Hilbert approach, which does not work for these kind of problems. As a prototypical example...
متن کاملA small dispersion limit to the Camassa-Holm equation: A numerical study
In this paper we take up the question of a small dispersion limit for the Camassa–Holm equation. The particular limit we study involves a modification of the Camassa–Holm equation, seen in the recent theoretical developments by Himonas and Misiołek, as well as the first author, where well-posedness is proved in weak Sobolev spaces. This work led naturally to the question of how solutions actual...
متن کاملOn the development of a high-order compact scheme for exhibiting the switching and dissipative solution natures in the Camassa-Holm equation
In this paper a two-step iterative solution algorithm for solving the Camassa–Holm equation, which involves only the first-order derivative term, is presented. In each set of the u P and u m differential equations, one is governed by the inviscid nonlinear convection–reaction equation for the time-evolving fluid velocity component along the horizontal direction. The other equation is known as t...
متن کاملConformal Properties and Bäcklund Transform for the Associated Camassa-Holm Equation
Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this paper. It is shown that the Bäcklund transform is...
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:
- SIAM J. Math. Analysis
دوره 41 شماره
صفحات -
تاریخ انتشار 2009