Factorization problem on the Hilbert-Schmidt group and the Camassa-Holm equation
نویسندگان
چکیده
منابع مشابه
On the Camassa-Holm equation
This talk is focused on recent progress of studies for the Camassa-Holm equation. First, we will give a brief review on the derivations, well-posedness for the strong solution, blow-up phenomenon and existence of the weak solutions. Then, infinite propagation speed for the Camassa-Holm equation will be proved in the following sense: the corresponding solution u(x, t) with compactly supported in...
متن کاملOn the isospectral problem of the dispersionless Camassa–Holm equation
We discuss direct and inverse spectral theory for the isospectral problem of the dispersionless Camassa–Holm equation, where the weight is allowed to be a finite signed measure. In particular, we prove that this weight is uniquely determined by the spectral data and solve the inverse spectral problem for the class of measures which are sign definite. The results are applied to deduce several fa...
متن کاملThe string density problem and the Camassa-Holm equation.
Recently, the string density problem, considered in the pioneering work of M. G. Kreĭn, has arisen naturally in connection with the Camassa-Holm equation for shallow water waves. In this paper we review the forward and inverse string density problems, with some numerical examples, and relate it to the Camassa-Holm equation, with special reference to multi-peakon/anti-peakon solutions. Under str...
متن کاملThe Camassa–Holm Equation and The String Density Problem
is an extensively studied nonlinear equation. It first appeared as an abstract biHamiltonian partial differential equation in an article of Fuchssteiner and Fokas [39] but did not receive much attention until Camassa and Holm [15] (see also [16]) derived it as a nonlinear wave equation that models unidirectional wave propagation on shallow water and discovered its rich mathematical structure. I...
متن کاملThe Spectral problem for the dispersionless Camassa-Holm equation
We present a spectral and inverse spectral theory for the zero dispersion spectral problem associated with the Camassa-Holm equation. This is an alternative approach to that in [10] by Eckhardt and Teschl. Mathematics Subject Classification (2010). Primary 37K15, 34B40 ; Secondary 35Q35, 34L05.
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2007
ISSN: 0010-3640,1097-0312
DOI: 10.1002/cpa.20207