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On nonlocal symmetries generated by recursion operators: Second-order evolution equations
| 1. | Division of Mathematics, Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden |
| 2. | Dipartimento di Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy |
We introduce a new type of recursion operator suitable to generate a class of nonlocal symmetries for those second-order evolution equations in $1+1$ dimension which allow the complete integration of their time-independent versions. We show that this class of evolution equations is $C$-integrable (linearizable by a point transformation). We also discuss some applications.
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N. Petersson, N. Euler and M. Euler,
Recursion Operators for a Class of Integrable ThirdOrder Evolution Equations, Stud. Appl. Math., 112 (2004), 201-225.
doi: 10.1111/j.0022-2526.2004.01511.x. |
show all references
References:
| [1] |
S. C. Anco and G. Bluman,
Direct construction method for conservation laws of PDEs Part Ⅱ: General treatment, Euro. J. Applied Mathematics, 13 (2002), 567-585.
doi: 10.1017/S0956792501004661. |
| [2] |
M. Euler and N. Euler,
Second-order recursion operators of third-order evolution equations with fourth-order integrating factors, J. Nonlinear Math. Phys., 14 (2007), 313-315.
doi: 10.2991/jnmp.2007.14.3.2. |
| [3] |
N. Euler and M. Euler,
On nonlocal symmetries, nonlocal conservation laws and nonlocal transformations of evolution equations: Two linearisable hierarchies, J. Nonlinear Math. Phys., 16 (2009), 489-504.
doi: 10.1142/S1402925109000509. |
| [4] |
M. Euler, N. Euler and N. Petersson,
Linearisable hierarchies of evolution equations in (1+1) dimensions, Stud. Appl. Math., 111 (2003), 315-337.
doi: 10.1111/1467-9590.t01-1-00236. |
| [5] |
A. S. Fokas,
Symmetries and Integrability, Stud. Appl. Math., 77 (1987), 253-299.
doi: 10.1002/sapm1987773253. |
| [6] |
P. J. Olver,
Evolution equations possessing infinitely many symmetries, J. Math. Phys., 18 (1977), 1212-1215.
doi: 10.1063/1.523393. |
| [7] |
P. J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, 1986.
doi: 10.1007/978-1-4684-0274-2. |
| [8] |
N. Petersson, N. Euler and M. Euler,
Recursion Operators for a Class of Integrable ThirdOrder Evolution Equations, Stud. Appl. Math., 112 (2004), 201-225.
doi: 10.1111/j.0022-2526.2004.01511.x. |
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