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The converse problem for the multipotentialisation of evolution equations and systems
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.
2011 (English)In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 18, no Suppl. 1, p. 77-105Article in journal (Refereed) Published
Abstract [en]

We propose a method to identify and classify evolution equations and systems that can be multipotentialised in given target equations or target systems. We refer to this as the converse problem. Although we mainly study a method for (1 + 1)-dimensional equations/system, we do also propose an extension of the methodology to higher-dimensional evolution equations. An important point is that the proposed converse method allows one to identify certain types of auto-Bäcklund transformations for the equations/systems. In this respect we define the triangular-auto-Bäcklund transformation and derive its connections to the converse problem. Several explicit examples are given. In particular, we investigate a class of linearisable third-order evolution equations, a fifth-order symmetry-integrable evolution equation as well as linearisable systems.

Place, publisher, year, edition, pages
2011. Vol. 18, no Suppl. 1, p. 77-105
Keywords [en]
Nonlinear evolution equations, potentialisation, auto-Bäcklund transformations, linearisation, the converse problem, Mathematics
Keywords [sv]
Matematik
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-3972DOI: 10.1142/S1402925111001295ISI: 000291405300006Scopus ID: 2-s2.0-79958721166Local ID: 1d32ad55-9997-44cd-9c70-2308b7d62c7cOAI: oai:DiVA.org:ltu-3972DiVA, id: diva2:976834
Note
Validerad; 2011; 20110610 (norbert)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Euler, NorbertEuler, Marianna

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