Zobrazeno 1 - 10
of 133
pro vyhledávání: '"Frank W. Nijhoff"'
Autor:
Frank W Nijhoff
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Vol Proceedings: OCNMP... (2024)
A variational structure for the potential AKP system is established using the novel formalism of a Lagrangian multiforms. The structure comprises not only the fully discrete equation on the 3D lattice, but also its semi-discrete variants including se
Externí odkaz:
https://doaj.org/article/6b7c504717774350a797d66eef80ed0a
Publikováno v:
Communications in Mathematical Physics. 399:599-650
We establish an infinite family of solutions in terms of elliptic functions of the lattice Boussinesq systems by setting up a direct linearisation scheme, which provides the solution structure for those equations in the elliptic case. The latter, whi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::602b7a41e9294a070f3776e378ce1d4a
https://doi.org/10.1007/s00220-022-04567-8
https://doi.org/10.1007/s00220-022-04567-8
Publikováno v:
International Mathematics Research Notices. 2023:1420-1460
We present, for the first time, a Lagrangian multiform for the complete Kadomtsev-Petviashvili (KP) hierarchy -- a single variational object that generates the whole hierarchy and encapsulates its integrability. By performing a reduction on this Lagr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::aa04dd96c8d910593ea82df3949d5d17
https://doi.org/10.1093/imrn/rnab288
https://doi.org/10.1093/imrn/rnab288
Autor:
Frank W. Nijhoff
A Lagrangian multiform structure is established for a generalisation of the Darboux system describing orthogonal curvilinear coordinate systems. It has been shown in the past that this system of coupled PDEs is in fact an encoding of the entire Kadom
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5d9cd97910f47fc86211c71e59c7acf2
http://arxiv.org/abs/2206.14338
http://arxiv.org/abs/2206.14338
Publikováno v:
Studies in Applied Mathematics. 146:233-278
In this paper we present novel integrable symplectic maps, associated with ordinary difference equations, and show how they determine, in a remarkably diverse manner, the integrability, including Lax pairs and the explicit solutions, for integrable p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::09559afe3d73d6534b5f6f21e3d0cc94
https://doi.org/10.1111/sapm.12346
https://doi.org/10.1111/sapm.12346
Autor:
Wei Fu, Frank W. Nijhoff
The coupled Kadomtsev--Petviashvili system associated with an elliptic curve, proposed by Date, Jimbo and Miwa [J. Phys. Soc. Jpn., 52:766--771, 1983], is reinvestigated within the direct linearisation framework, which provides us with more insights
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eeaa901b80cec99874e33f7afabb82f1
The discrete-time Toda equation arises as a universal equation for the relevant Hankel determinants associated with one-variable orthogonal polynomials through the mechanism of adjacency, which amounts to the inclusion of shifted weight functions in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2165040d9a4743070fe923099a165898
Autor:
Peter A. Clarkson, Frank W. Nijhoff
There has in recent years been a remarkable growth of interest in the area of discrete integrable systems. Much progress has been made by applying symmetry groups to the study of differential equations, and connections have been made to other topics
Autor:
Frank W. Nijhoff, Wei Fu
Publikováno v:
Nonlinear Systems and Their Remarkable Mathematical Structures ISBN: 9781003087670
Nonlinear Systems and Their Remarkable Mathematical Structures
Nonlinear Systems and Their Remarkable Mathematical Structures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::47c6c74db96a56e8c6f59f717470443d
https://doi.org/10.1201/9781003087670-2
https://doi.org/10.1201/9781003087670-2
The Q1 lattice equation, a member in the Adler–Bobenko–Suris list of 3D consistent lattices, is investigated. By using the multidimensional consistency, a novel Lax pair for Q1 equation is given, which can be nonlinearized to produce integrable s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::403805570c7f210a46ed1460db87b949
http://arxiv.org/abs/2005.12765
http://arxiv.org/abs/2005.12765