TY - JOUR
T1 - Pöppe triple systems and integrable equations
AU - Doikou, Anastasia
AU - Malham, Simon J. A.
AU - Stylianidis, Ioannis
AU - Wiese, Anke
N1 - 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:
© 2023
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 - http://www.scopus.com/inward/record.url?scp=85173046651&partnerID=8YFLogxK
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 -