Zobrazeno 1 - 10
of 141
pro vyhledávání: '"Dimakis, Aristophanes"'
Autor:
Dimakis, Aristophanes, Korepanov, Igor
Publikováno v:
J. Math. Phys. 62, 051701 (2021)
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 structure of (2n+1)-gon and 2n-simplex equations in direct sums of vector spa
Externí odkaz:
http://arxiv.org/abs/2009.02352
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 of a matrix KP equation. Using the Lax matrix and its inverse, a relate
Externí odkaz:
http://arxiv.org/abs/2001.09688
Publikováno v:
Physica Scripta, 2018
We study soliton solutions of matrix "good" Boussinesq equations, generated via a binary Darboux transformation. Essential features of these solutions are revealed via their "tropical limit", as exploited in previous work about the KP equation. This
Externí odkaz:
http://arxiv.org/abs/1805.09711
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 Backlund and (forward, backward and binary) Darboux transformations f
Externí odkaz:
http://arxiv.org/abs/1801.00589
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 of soliton solutions whose tropical limit graph has the form of a root
Externí odkaz:
http://arxiv.org/abs/1709.09848
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 attached to its constituting lines. There is a subclass of "pure line soliton
Externí odkaz:
http://arxiv.org/abs/1708.05694
We reveal the origin and structure of self-consistent source extensions of integrable equations from the perspective of binary Darboux transformations. They arise via a deformation of the potential that is central in this method. As examples, we obta
Externí odkaz:
http://arxiv.org/abs/1510.05166
Publikováno v:
SIGMA 11 (2015), 042, pp. 49
It is shown that higher Bruhat orders admit a decomposition into a higher Tamari order, the corresponding dual Tamari order, and a "mixed order." We describe simplex equations (including the Yang-Baxter equation) as realizations of higher Bruhat orde
Externí odkaz:
http://arxiv.org/abs/1409.7855
Via a "tropical limit" (Maslov dequantization), Korteweg-deVries (KdV) solitons correspond to piecewise linear graphs in two-dimensional space-time. We explore this limit.
Comment: 10 pages, 4 figures, conference "Physics and Mathematics of Nonl
Comment: 10 pages, 4 figures, conference "Physics and Mathematics of Nonl
Externí odkaz:
http://arxiv.org/abs/1308.1545
Publikováno v:
SIGMA 9 (2013), 009, 31 pages
We present a general solution-generating result within the bidifferential calculus approach to integrable partial differential and difference equations, based on a binary Darboux-type transformation. This is then applied to the non-autonomous chiral
Externí odkaz:
http://arxiv.org/abs/1207.1308