Abstract
The two-component Camassa–Holm system and two-component Hunter–Saxton system are completely integrable models. In this paper, it is shown that these systems admit nonlocal symmetries by their geometric integrability. As an application, we obtain the recursion operator and conservation laws by using this kind of nonlocal symmetries.
Highlights
IntroductionNonlocal Symmetries of TwoComponent Camassa–Holm and Hunter–Saxton Systems
We have shown that the two-component Camassa–Holm system and the two-component
Hunter–Saxton system admit a class of nonlocal symmetries, and the recursion operator of the two-component Camassa–Holm system is constructed by using its potential variables
Summary
Nonlocal Symmetries of TwoComponent Camassa–Holm and Hunter–Saxton Systems. This paper mainly discusses nonlocal symmetries, conservation laws, and recursion operators of the two-component Camassa–Holm system [1,2] and the two-component. These systems have Lax-pairs and bi-Hamiltonian structures, which are completely integrable systems. It is very important to study the nonlocal symmetries of integrable equations. We obtain the recursion operator and conservation laws by using this kind of nonlocal symmetries. Fokas and Fuchssteiner [4] obtained the Camassa–Holm equation through the integrability of the.
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