Pöppe triple systems and integrable equations

Anastasia Doikou; Simon J. A. Malham; Ioannis Stylianidis; Anke Wiese

doi:10.1016/j.padiff.2023.100565

Pöppe triple systems and integrable equations

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

30 Downloads (Pure)

Abstract

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.

Original language	English
Article number	100565
Journal	Partial Differential Equations in Applied Mathematics
Volume	8
Early online date	27 Sept 2023
DOIs	https://doi.org/10.1016/j.padiff.2023.100565
Publication status	Published - Dec 2023

Keywords

Modified Korteweg–de Vries equation
Nonlinear Schrödinger equation
Triple system

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.padiff.2023.100565Licence: CC BY

Download pdf
© 2023 The Authors.
Final published version, 625 KBLicence: CC BY

Cite this

@article{bf9044039be744b6aa9fb64fdac3a8ff,

title = "P{\"o}ppe triple systems and integrable equations",

abstract = "We construct the combinatorial P{\"o}ppe triple system, or ternary algebra, that underlies the non-commutative nonlinear Schr{\"o}dinger (NLS) and modified Korteweg–de Vries (mKdV) hierarchy. We demonstrate that the P{\"o}ppe 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 P{\"o}ppe 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.",

keywords = "Modified Korteweg–de Vries equation, Nonlinear Schr{\"o}dinger equation, Triple system",

author = "Anastasia Doikou and Malham, \{Simon J. A.\} and Ioannis Stylianidis and Anke Wiese",

note = "Funding Information: SJAM was supported by an EPSRC Mathematical Sciences Small Grant EP/X018784/1 . IS was supported by an EPSRC DTA Scholarship . Publisher Copyright: {\textcopyright} 2023",

year = "2023",

month = dec,

doi = "10.1016/j.padiff.2023.100565",

language = "English",

volume = "8",

journal = "Partial Differential Equations in Applied Mathematics",

issn = "2666-8181",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Pöppe triple systems and integrable equations

AU - Doikou, Anastasia

AU - Malham, Simon J. A.

AU - Stylianidis, Ioannis

AU - Wiese, Anke

PY - 2023/12

Y1 - 2023/12

N2 - 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.

AB - 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.

KW - Modified Korteweg–de Vries equation

KW - Nonlinear Schrödinger equation

KW - Triple system

UR - https://www.scopus.com/pages/publications/85173046651

U2 - 10.1016/j.padiff.2023.100565

DO - 10.1016/j.padiff.2023.100565

M3 - Article

SN - 2666-8181

VL - 8

JO - Partial Differential Equations in Applied Mathematics

JF - Partial Differential Equations in Applied Mathematics

M1 - 100565

ER -

Pöppe triple systems and integrable equations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this