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arXiv · 1011.2623

The converse problem for the multipotentialisation of evolution equations and systems

Norbert Euler·Marianna Euler
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Abstract

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 {\it 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-B\"acklund transformations for the equations/systems. In this respect we define the {\it triangular-auto-B\"acklund 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.

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Norbert Euler, Marianna Euler. 2010-11-11. The converse problem for the multipotentialisation of evolution equations and systems. https://doi.org/10.1142/s1402925111001295

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