The Scattering Approach for the Camassa–Holm equation
نویسندگان
چکیده
We present an approach proving the integrability of the Camassa–Holm equation for initial data of small amplitude.
منابع مشابه
On the Inverse Scattering Approach to the Camassa-Holm Equation
A simple algoritm for the inverse scattering approach to the Camassa-Holm equation is presented.
متن کاملOn 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 کاملInverse Scattering Transform for the Camassa-Holm equation
An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data. The main difference with respect to the standard Inverse Scattering Transform lies in the fact that we have a weighted spectral problem. We therefore have to develop different asy...
متن کاملPoisson structure and Action-Angle variables for the Camassa-Holm equation
The Poisson brackets for the scattering data of the Camassa-Holm equation are computed. Consequently, the action-angle variables are expressed in terms of the scattering data. PACS: 02.30.Ik, 05.45.Yv, 45.20.Jj, 02.30.Jr
متن کاملGeneralised Fourier transform for the Camassa-Holm hierarchy
The squared eigenfunctions of the spectral problem associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform for the Camassa-Holm hierarchy as a Generalised Fourier transform. The main result of this work is the derivation of the completeness relation for the squared solutions of the Camassa-Holm spectral problem. W...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002