Nonlocal Symmetries of the Camassa-Holm Type Equations |
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| Authors: | Lu ZHAO and Changzheng QU |
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| Institution: | Center for Nonlinear Studies and Department of Mathematics,Ningbo University, Ningbo 315211, Zhejiang, China. and Center for Nonlinear Studies and Department of Mathematics,Ningbo University, Ningbo 315211, Zhejiang, China. |
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| Abstract: | A class of nonlocal symmetries of the Camassa-Holm type equations
with bi-Hamiltonian structures, including the Camassa-Holm equation,
the modified Camassa-Holm equation, Novikov equation and
Degasperis-Procesi equation, is studied. The nonlocal symmetries are
derived by looking for the kernels of the recursion operators and
their inverse operators of these equations. To find the kernels of
the recursion operators, the authors adapt the known
factorization results for the recursion operators of the KdV,
modified KdV, Sawada-Kotera and Kaup-Kupershmidt hierarchies, and the
explicit Liouville correspondences between the KdV and Camassa-Holm
hierarchies, the modified KdV and modified Camassa-Holm hierarchies,
the Novikov and Sawada-Kotera hierarchies, as well as the
Degasperis-Procesi and Kaup-Kupershmidt hierarchies. |
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| Keywords: | Nonlocal symmetry Recursion operator Camassa-Holm equation Modified Camassa-Holm equation Novikov equation Degasperis-Procesi equation Liouvillecorrespondence |
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