
 
Nonlocal Symmetries of the CamassaHolm Type Equations 
 
Citation： 
Lu ZHAO,Changzheng QU.Nonlocal Symmetries of the CamassaHolm Type Equations[J].Chinese Annals of Mathematics B,2020,41(3):407~418 
Page view： 32
Net amount： 25 
Authors： 
Lu ZHAO; Changzheng QU 
Foundation： 
This work was supported by the National Natural Science
Foundation of China (Nos.11631107, 11471174). 


Abstract： 
A class of nonlocal symmetries of the CamassaHolm type equations
with biHamiltonian structures, including the CamassaHolm equation,
the modified CamassaHolm equation, Novikov equation and
DegasperisProcesi 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, SawadaKotera and KaupKupershmidt hierarchies, and the
explicit Liouville correspondences between the KdV and CamassaHolm
hierarchies, the modified KdV and modified CamassaHolm hierarchies,
the Novikov and SawadaKotera hierarchies, as well as the
DegasperisProcesi and KaupKupershmidt hierarchies. 
Keywords： 
Nonlocal symmetry, Recursion operator, CamassaHolm equation, Modified CamassaHolm equation, Novikov equation, DegasperisProcesi equation, Liouvillecorrespondence 
Classification： 
37K05, 37K10 

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