The Converse Problem for the Multipotentialisation of Evolution Equations and Systems
- 10.1142/S1402925111001295How to use a DOI?
- Nonlinear evolution equations; potentialisation; auto-Bäcklund transformations; linearisation; the converse problem
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.
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Norbert Euler AU - Marianna Euler PY - 2021 DA - 2021/01/07 TI - The Converse Problem for the Multipotentialisation of Evolution Equations and Systems JO - Journal of Nonlinear Mathematical Physics SP - 77 EP - 105 VL - 18 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001295 DO - 10.1142/S1402925111001295 ID - Euler2021 ER -