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Recursion Operators for a Class of Integrable Third‐Order Evolution Equations
Author(s) -
Petersson Niclas,
Euler Norbert,
Euler Marianna
Publication year - 2004
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.0022-2526.2004.01511.x
Subject(s) - hodograph , homogeneous space , integrable system , mathematics , recursion (computer science) , order (exchange) , mathematical physics , class (philosophy) , pure mathematics , mathematical analysis , geometry , finance , algorithm , artificial intelligence , computer science , economics
We consider u t = u α u xxx + n ( u ) u x u xx + m ( u ) u 3 x + r ( u ) u xx + p ( u ) u 2 x + q ( u ) u x + s ( u ) with α= 0 and α= 3 , for those functional forms of m , n , p , q , r , s for which the equation is integrable in the sense of an infinite number of Lie‐Bäcklund symmetries. Recursion operators which are x ‐ and t ‐independent that generate these infinite sets of (local) symmetries are obtained for the equations. A combination of potential forms, hodograph transformations, and x ‐generalized hodograph transformations are applied to the obtained equations.