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A new kind of nonlocal symmetry for the μ ‐Camassa‐Holm equation with linear dispersion
Author(s) -
Shi Zhenhua,
Du Jingjing
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5343
Subject(s) - camassa–holm equation , mathematics , integrable system , transformation (genetics) , symmetry (geometry) , quadratic equation , conservation law , homogeneous space , mathematical physics , dispersion (optics) , mathematical analysis , recursion (computer science) , operator (biology) , construct (python library) , physics , quantum mechanics , geometry , biochemistry , chemistry , algorithm , repressor , transcription factor , gene , computer science , programming language
The μ ‐Camassa‐Holm equation with linear dispersion is a completely integrable model. In this paper, it is shown that this equation has quadratic pseudo‐potentials that allow us to construct pseudo‐potential–type nonlocal symmetries. As an application, we obtain its recursion operator by using this kind of nonlocal symmetry, and we construct a Darboux transformation for the μ ‐Camassa‐Holm equation.