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

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