منابع مشابه
Peakon-Antipeakon Interaction
Explicit formulas are given for the multi-peakon-antipeakon solutions of the Camassa– Holm equation, and a detailed analysis is made of both short-term and long-term aspects of the interaction between a single peakon and single anti-peakon. The strongly nonlinear equation ( 1 − 1 4 D ) ut = 3 2 ( u ) x − 1 8 ( u2x ) x − 1 4 (uuxx)x, (1) introduced by Camassa and Holm [5] as a possible model for...
متن کاملA New Integrable Equation with Peakon Solutions
We consider a new partial differential equation, of a similar form to the Camassa-Holm shallow water wave equation, which was recently obtained by Degasperis and Procesi using the method of asymptotic integrability. We prove the exact integrability of the new equation by constructing its Lax pair, and we explain its connection with a negative flow in the Kaup-Kupershmidt hierarchy via a recipro...
متن کاملGeodesic Flow on Extended Bott-Virasoro Group and Generalized Two Component Peakon Type Dual Systems
This paper discusses several algorithmic ways of constructing integrable evolution equations based on Lie algebraic structure. We derive, in a pedagogical style, a large class of two component peakon type dual systems from their two component soliton equations counter part. We study the essential aspects of Hamiltonian flows on coadjoint orbits of the centrally extended semidirect product group...
متن کاملG - Strands and Peakon Collisions on Diff ( R ) ?
A G-strand is a map g : R × R → G for a Lie group G that follows from Hamilton’s principle for a certain class of G-invariant Lagrangians. Some G-strands on finite-dimensional groups satisfy 1 + 1 space-time evolutionary equations that admit soliton solutions as completely integrable Hamiltonian systems. For example, the SO(3)-strand equations may be regarded physically as integrable dynamics f...
متن کاملVirasoro Action on Pseudo-differential Symbols and (Noncommutative) Supersymmetric Peakon Type Integrable Systems
Using Grozman’s formalism of invariant differential operators we demonstrate the derivation of N = 2 Camassa-Holm equation from the action of V ect(S1|2) on the space of pseudo-differential symbols. We also use generalized logarithmic 2-cocycles to derive N = 2 super KdV equations. We show this method is equally effective to derive Camassa-Holm family of equations and these system of equations ...
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ژورنال
عنوان ژورنال: Chinese Physics Letters
سال: 2017
ISSN: 0256-307X,1741-3540
DOI: 10.1088/0256-307x/34/10/100201