From NLS type matrix refactorisation problems to set-theoretical solutions of the 2- and 3-simplex equations

2025/04/29 by Sotiris Konstantinou-Rizos, Konstantinou-Rizos, Sotiris · 1 voice
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #nlin.SI

paper · pdf · doi:10.48550/arxiv.2504.21094

Abstract

We present a method for constructing hierarchies of solutions to n-simplex equations by variating the spectral parameter in their Lax representation. We use this method to derive new solutions to the set-theoretical 2- and 3-simplex equations which are related to the Adler map and Nonlinear Schrödinger (NLS) type equations. Moreover, we prove that some of the derived Yang--Baxter maps are completely integrable.

Citations

• On quadrirational pentagon maps
• Yang--Baxter maps of KdV, NLS and DNLS type on division rings
• Entwining Yang-Baxter maps over Grassmann algebras
• Electric network and Hirota type 4-simplex maps
• Nonlinear Schrödinger type tetrahedron maps
• Grassmann extensions of Yang-Baxter maps
• Darboux transformation for the vector sine-Gordon equation and integrable equations on a sphere
• Simplex and Polygon Equations
• Non-commutative rational Yang-Baxter maps
• Darboux transformations, finite reduction groups and related Yang-Baxter maps
• Families of Integrable Equations
• On non-multiaffine consistent-around-the-cube lattice equations
• Yang Baxter maps with first degree polynomial 2 by 2 Lax matrices
• Yang-Baxter maps and multi-field integrable lattice equations
• Yang-Baxter maps and symmetries of integrable equations on quad-graphs
• Quasi-Hopf *-Algebras
• Functional Tetrahedron Equation
• Algebraic integrable dynamical systems, 2+1-dimensional models in wholly discrete space-time, and inhomogeneous models in 2-dimensional statistical physics

Discussions

• Sotiris Konstantinou-Rizos: From NLS type matrix refactorisation problems to set-theoretical solutions of the 2- and 3-simplex equations https://arxiv.org/abs/2504.21094 https://arxiv.org/pdf/2504.210 [bsky, 0 points, 1 comments]

Related

• Scalene Yang-Baxter maps and Lax triples
• Set-theoretical solutions of simplex equations
• Yang-Baxter maps and matrix solitons
• Yang--Baxter maps of KdV, NLS and DNLS type on division rings
• Entwining Yang-Baxter maps and integrable lattices