Pöppe triple systems and integrable equations

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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 languageEnglish
Article number100565
JournalPartial Differential Equations in Applied Mathematics
Early online date27 Sept 2023
Publication statusPublished - Dec 2023


  • Modified Korteweg–de Vries equation
  • Nonlinear Schrödinger equation
  • Triple system

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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