Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Vassilios G. Papageorgiou"'
A relationship between the tetrahedron equation for maps and the consistency property of integrable discrete equations on $\mathbb{Z}^3$ is investigated. Our approach is a generalization of a method developed in the context of Yang-Baxter maps, based
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4122cdf774b43e22573790550544b00e
http://arxiv.org/abs/1908.03019
http://arxiv.org/abs/1908.03019
Publikováno v:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 476:20190668
We present two lists of two-component systems of integrable difference equations defined on the edges of the Z 2 graph. The integrability of these systems is manifested by their Lax formulation which is a consequence of the multi-dimensional compatib
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d0cac2766d1d904721214b14272451bb
https://doi.org/10.1098/rspa.2019.0668
https://doi.org/10.1098/rspa.2019.0668
Publikováno v:
Physica D: Nonlinear Phenomena. 238:273-289
We study the Anisotropic Stormer Problem (ASP) and the Isosceles Three-Body Problem (IP), from the viewpoint of integrability, using Morales–Ramis theory and its generalization. The study of their integrability presents particular interest since th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::16fb1f58643e835b251c931f663e0744
https://doi.org/10.1016/j.physd.2008.10.010
https://doi.org/10.1016/j.physd.2008.10.010
Publikováno v:
Journal of Physics A: Mathematical and Theoretical. 40:12619-12627
We construct special solutions of the Hirota–Miwa equation for which the τ-function is a polynomial in the independent variables. Three different methods are presented: direct construction (obtained also as a limit of the soliton solutions), and t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::35c032eb09a908a4a6d448904e8a4238
https://doi.org/10.1088/1751-8113/40/42/s08
https://doi.org/10.1088/1751-8113/40/42/s08
Publikováno v:
Journal of Physics A: Mathematical and Theoretical. 40:12677-12690
A variety of Yang-Baxter maps are obtained from integrable multi-field equations on quad-graphs. A systematic framework for investigating this connection relies on the symmetry groups of the equations. The method is applied to lattice equations intro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ec6d7b77c0722bc98fe7349f49ee4b8c
https://doi.org/10.1088/1751-8113/40/42/s12
https://doi.org/10.1088/1751-8113/40/42/s12
Publikováno v:
Physics Letters A. 235:475-479
We propose a discrete analog of the dressing transformation. Our starting point is a variant of the quotient-difference algorithm which, in this case, corresponds to a linear problem with shifts in the eigenvalues. The proper periodicity conditions l
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::27a4ad3815f0b91c8fb18c6a1cf4a73e
https://doi.org/10.1016/s0375-9601(97)00640-3
https://doi.org/10.1016/s0375-9601(97)00640-3
Publikováno v:
Physica A: Statistical Mechanics and its Applications. 228:172-188
A new class of integrable lattice systems is introduced which are the time-discretisations of the Bogoyavlensky systems. Finite-dimensional reductions of these systems are considered that give rise to integrable mappings. Furthermore, the similarity
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f007e45d92ed43285498587973cd6cc1
https://doi.org/10.1016/0378-4371(95)00440-8
https://doi.org/10.1016/0378-4371(95)00440-8
Publikováno v:
Letters in Mathematical Physics. 34:91-101
Using orthogonal polynomial theory, we construct the Lax pair for the quotient-difference algorithm in the natural Rutishauser variables. We start by considering the family of orthogonal polynomials corresponding to a given linear form. Shifts on the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1ff157b9c7f41e06b86397f27a0d0909
https://doi.org/10.1007/bf00739089
https://doi.org/10.1007/bf00739089
According to Shibukawa, ternary systems defined on quasigroups and satisfying certain conditions provide a way of constructing dynamical Yang-Baxter maps. After noticing that these conditions can be interpreted as 3-dimensional compatibility of equat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d92d21a15d277445de8b74013b72755e
http://arxiv.org/abs/1203.2037
http://arxiv.org/abs/1203.2037
A construction of multidimensional parametric Yang-Baxter maps is presented. The corresponding Lax matrices are the symplectic leaves of first degree matrix polynomials equipped with the Sklyanin bracket. These maps are symplectic with respect to the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::813fdfee7bfe9486b0c3de866a5c1b66
http://arxiv.org/abs/1106.0214
http://arxiv.org/abs/1106.0214