On nonlocal symmetries generated by recursion operators: Second-order evolution equations

M. Euler; N. Euler; M. C. Nucci

doi:10.3934/dcds.2017181

Article Contents

2017, Volume 37, Issue 8: 4239-4247. Doi: 10.3934/dcds.2017181

This issue Previous Article Separated nets arising from certain higher rank $\mathbb{R}^k$ actions on homogeneous spaces Next Article The geometric discretisation of the Suslov problem: A case study of consistency for nonholonomic integrators

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

^* Corresponding author: norbert@ltu.se
^* Corresponding author: norbert@ltu.se

Received: February 2017

Revised: May 2017

Published: May 2017

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Abstract

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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Mathematics Subject Classification: Primary: 35G20, 35A30, 58J70.

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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.