Zobrazeno 1 - 10
of 190
pro vyhledávání: '"Alfred Ramani"'
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Vol Proceedings: OCNMP... (2024)
We study the link between the degree growth of integrable birational mappings of order higher than two and their singularity structures. The higher order mappings we use in this study are all obtained by coupling mappings that are integrable through
Externí odkaz:
https://doaj.org/article/e151a3e05ae64ca889312fe8fb737019
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Vol Volume 3 (2023)
We present a method for the construction of the trajectory of a discrete Painlev\'e equation associated with the affine Weyl group E$_8^{(1)}$ on the weight lattice of said group. The method is based on the geometrical description of the lattice and
Externí odkaz:
https://doaj.org/article/93c998dad0e84ebab541dddc4c989773
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 4, p 051 (2008)
We examine quantum extensions of the continuous Painlevé equations, expressed as systems of first-order differential equations for non-commuting objects. We focus on the Painlevé equations II, IV and V. From their auto-Bäcklund transformations we
Externí odkaz:
https://doaj.org/article/2529be4b98ae4bccafab00775833fb97
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 3, p 073 (2007)
We examine whether the Painlevé property is necessary for the integrability of partial differential equations (PDEs). We show that in analogy to what happens in the case of ordinary differential equations (ODEs) there exists a class of PDEs, integra
Externí odkaz:
https://doaj.org/article/b12c51de401a451f95a3d7e2ff21714e
Publikováno v:
J.Phys.A
J.Phys.A, 2021, 54 (9), pp.095201. ⟨10.1088/1751-8121/abd8f4⟩
J.Phys.A, 2021, 54 (9), pp.095201. ⟨10.1088/1751-8121/abd8f4⟩
We study the structure of singularities in the discrete Korteweg–deVries (d-KdV) equation. Four different types of singularities are identified. The first type corresponds to localised, ‘confined’, singularities, the confinement constraints for
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::21fa111aef40144574ed8fdbe1e1d0ad
https://hal.archives-ouvertes.fr/hal-03143581
https://hal.archives-ouvertes.fr/hal-03143581
Publikováno v:
J.Phys.
J.Phys., 2020, 53 (A11), pp.114001. ⟨10.1088/1751-8121/ab72af⟩
J.Phys., 2020, 53 (A11), pp.114001. ⟨10.1088/1751-8121/ab72af⟩
The discrete KdV (dKdV) equation, the pinnacle of discrete integrability, is often thought to possess the singularity confinement property because it confines on an elementary quadrilateral. Here we investigate the singularity structure of the dKdV e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8c7212b2ba142f939e3d2ec52927548f
https://hal.archives-ouvertes.fr/hal-02879518
https://hal.archives-ouvertes.fr/hal-02879518
Publikováno v:
J.Phys.A
J.Phys.A, 2019, 52 (20), pp.205201. ⟨10.1088/1751-8121/ab1433⟩
J.Phys.A, 2019, 52 (20), pp.205201. ⟨10.1088/1751-8121/ab1433⟩
In this paper we present a rigorous method for deciding whether a birational three point mapping that has the singularity confinement property is integrable or not, based only on the structure of its (confined) singularity patterns. We also explain h
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::65a332e1839b2f5faa30fbda739713ad
https://hal.archives-ouvertes.fr/hal-02116519
https://hal.archives-ouvertes.fr/hal-02116519
Publikováno v:
Journal of Nonlinear Mathematical Physics. 18:75
We present a new method for the derivation of mappings of HKY type. These are second-order mappings which do not have a biquadratic invariant like the QRT mappings, but rather an invariant of degree higher than two in at least one of the variables. O
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::883673ab79941b1a598b685face45705
https://doi.org/10.1142/s1402925111001179
https://doi.org/10.1142/s1402925111001179
Publikováno v:
Journal of Nonlinear Mathematical Physics. 20:565
We introduce the Schlesinger transformations for the Gambier, linearisable, equation and by combining the former construct the contiguity relations of the solutions of the latter. We extend the approach to the discrete domain obtaining thus the Schle
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e0804e4d952901ff927fe44a70e5e07a
https://doi.org/10.1080/14029251.2013.868269
https://doi.org/10.1080/14029251.2013.868269
Autor:
B. Grammaticos, Alfred Ramani
Publikováno v:
Journal of Nonlinear Mathematical Physics. 20:153
We derive discrete systems which result from a second, not studied up to now, form of the q-PVI equation. The derivation is based on two different procedures: “limits” and “degeneracies”. We obtain several new discrete Painleve equations alon
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8d818feed6ff2851917cb93cae06598c
https://doi.org/10.1080/14029251.2013.862444
https://doi.org/10.1080/14029251.2013.862444