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Nonlocal invariance of the multipotentialisations of the Kupershmidt equation and its higher-order hierarchies
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0003-0370-7274
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2018 (English)In: Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 1 / [ed] Norbert Euler, Boca Raton, USA: CRC Press, 2018, 1, p. 317-351Chapter in book (Refereed)
Abstract [en]

The term multipotentialisation of evolution equations in 1+1 dimensions refers to the process of potentialising a given evolution equation, followed by at least one further potentialisation of the resulting potential equation. For certain equations this process can be applied several times to result in a finite chain of potential equations, where each equation in the chain is a potential equation of the previous equation. By a potentialisation of an equation with dependent variable u to an equation with dependent variable v, we mean a differential substitution v_x=\Phi^t, where \Phi^t is a conserved current of the equation in u. The process of multipotentialisation may lead to interesting nonlocal transformations between the equations. Remarkably, this can, in some cases, result in nonlocal invariance transformations for the equations, which then serve as iteration formulas by which solutions can be generated for all the equations in the chain.

In the current paper we give a comprehensive introduction to this subject and report new nonlocal invariance transformations that result from the multipotentialisation of the Kupershmidt equation and its higher-order hierarchies. The recursion operators that define the hierarchies are given explicitly.

Place, publisher, year, edition, pages
Boca Raton, USA: CRC Press, 2018, 1. p. 317-351
Keywords [en]
Nonlinear Partial Differential Equations, Integrable Equations, Invariance
National Category
Natural Sciences Mathematics
Mathematics
Identifiers
ISBN: 9781138601000 (print)OAI: oai:DiVA.org:ltu-70947DiVA, id: diva2:1250257
Available from: 2018-09-22 Created: 2018-09-22 Last updated: 2019-07-09

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https://www.crcpress.com/Nonlinear-Systems-and-Their-Remarkable-Mathematical-Structures/Euler/p/book/9781138601000

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Euler, NorbertEuler, Marianna

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Cite
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