Pöppe triple systems and integrable equations

We construct the combinatorial Pöppe triple system, or ternary algebra, that underlies the non-commutative nonlinear Schrödinger (NLS) and modified Korteweg–de Vries (mKdV) hierarchy. We demonstrate that the Pöppe triple system provides an effective and systematic procedure for establishing that the...

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Bibliographic Details
Published in:Partial Differential Equations in Applied Mathematics
Main Authors: Anastasia Doikou, Simon J.A. Malham, Ioannis Stylianidis, Anke Wiese
Format: Article
Language:English
Published: Elsevier 2023-12-01
Subjects:
Nonlinear Schrödinger equation
Modified Korteweg–de Vries equation
Triple system
Online Access:http://www.sciencedirect.com/science/article/pii/S2666818123000785
Description
Summary:We construct the combinatorial Pöppe triple system, or ternary algebra, that underlies the non-commutative nonlinear Schrödinger (NLS) and modified Korteweg–de Vries (mKdV) hierarchy. We demonstrate that the Pöppe triple system provides an effective and systematic procedure for establishing that the NLS and mKdV equations are directly linearisable, which, in principle, extends to the whole hierarchy. This naturally extends the combinatorial Pöppe algebra, recently used to constructively establish integrability and uniqueness for the whole non-commutative potential Korteweg–de Vries hierarchy, to the NLS and mKdV hierarchy.
ISSN:2666-8181

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