98 citations · 1.1k across the 70 of their papers we have counts for
72 papers
Grassmannian-parameterized solutions to direct-sum polygon and simplex equations
Aristophanes Dimakis, Igor Korepanov
We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) and Yang--Baxter (2-simplex), respectively. We examine the general structu…
Tropical limit of matrix solitons and entwining Yang-Baxter maps
Aristophanes Dimakis, Folkert Müller-Hoissen
We consider a matrix refactorization problem, i.e., a "Lax representation", for the Yang-Baxter map that originated as the map of polarizations from the "pure" 2-soliton solution o…
Matrix Boussinesq solitons and their tropical limit
Aristophanes Dimakis, Folkert Müller-Hoissen, Xiao-Min Chen
We study soliton solutions of matrix "good" Boussinesq equations, generated via a binary Darboux transformation. Essential features of these solutions are revealed via their "tropi…
Differential Calculi on Associative Algebras and Integrable Systems
Aristophanes Dimakis, Folkert Müller-Hoissen
After an introduction to some aspects of bidifferential calculus on associative algebras, we focus on the notion of a "symmetry" of a generalized zero curvature equation and derive…
Matrix KP: tropical limit, Yang-Baxter and pentagon maps
Aristophanes Dimakis, Folkert Müller-Hoissen
In the tropical limit of matrix KP-II solitons, their support at fixed time is a planar graph with "polarizations" attached to its linear parts. In this work we explore a subclass…
Matrix KP: tropical limit and Yang-Baxter maps
Aristophanes Dimakis, Folkert Müller-Hoissen
We study soliton solutions of matrix Kadomtsev-Petviashvili (KP) equations in a tropical limit, in which their support at fixed time is a planar graph and polarizations are attache…