Dark Equations and Their Light Integrability

DOI

10.1080/14029251.2014.936760How to use a DOI?

Keywords

Burgers type system; differential-algebraic approach; asymptotic analysis; conserved quantities; Lax integrability; symmetry recursion operator; commuting infinite hierarchies of dynamical systems

Abstract

A relatively new approach to analyzing integrability, based upon differential-algebraic and symplectic techniques, is applied to some “dark equations ”of the type introduced by Boris Kupershmidt. These dark equations have unusual properties and are not particularly well-understood. In particular, dark three-component polynomial Burgers type systems are studied in detail. Their matrix Lax representations are constructed, and the related symmetry recursion operators and infinite hierarchies of integrable nonlinear dynamical systems along with their Lax representations are derived. New linear Lax spectral problems for dark integrable countable hierarchies of dynamical systems are proposed and some special cases are considered as a means of indicating that the approach presented is applicable to a far wider class of dark equations than analyzed here.

Copyright

© 2014 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/).

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TY  - JOUR
AU  - Denis Blackmore
AU  - Anatolij K. Prykarpatski
PY  - 2021
DA  - 2021/01/06
TI  - Dark Equations and Their Light Integrability
JO  - Journal of Nonlinear Mathematical Physics
SP  - 407
EP  - 428
VL  - 21
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2014.936760
DO  - 10.1080/14029251.2014.936760
ID  - Blackmore2021
ER  -