Zobrazeno 1 - 10
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pro vyhledávání: '"Nijhoff, F. W."'
Introduced in 2012, by Zhang, Zhao, and Nijhoff, the trilinear Boussinesq equation is the natural form of the equation for the $\tau$-function of the lattice Boussinesq system. In this paper we study various aspects of this equation: its highly nontr
Externí odkaz:
http://arxiv.org/abs/2407.11175
Autor:
Nijhoff, F. W., Zhang, D. J.
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Special Issue in Memory of Decio Levi (February 15, 2024) ocnmp:12759
The lattice Boussinesq (lBSQ) equation is a member of the lattice Gel'fand-Dikii (lGD) hierarchy, introduced in \cite{NijPapCapQui1992}, which is an infinite family of integrable systems of partial difference equations labelled by an integer $N$, whe
Externí odkaz:
http://arxiv.org/abs/2312.12684
Publikováno v:
Lett Math Phys 110, 805-826 (2020)
By considering the closure property of a Lagrangian multiform as a conservation law, we use Noether's theorem to show that every variational symmetry of a Lagrangian leads to a Lagrangian multiform. In doing so, we provide a systematic method for con
Externí odkaz:
http://arxiv.org/abs/1906.05084
Publikováno v:
J. Geom. Phys. 142 (2019), 66-79
It is shown that the Zakharov-Mihailov (ZM) Lagrangian structure for integrable nonlinear equations derived from a general class of Lax pairs possesses a Lagrangian multiform structure. We show that, as a consequence of this multiform structure, we c
Externí odkaz:
http://arxiv.org/abs/1812.08648
A general elliptic $N\times N$ matrix Lax scheme is presented, leading to two classes of elliptic lattice systems, one which we interpret as the higher-rank analogue of the Landau-Lifschitz equations, while the other class we characterize as the high
Externí odkaz:
http://arxiv.org/abs/1405.3927
We present a hierarchy of discrete systems whose first members are the lattice modified Korteweg-de Vries equation, and the lattice modified Boussinesq equation. The N-th member in the hierarchy is an N-component system defined on an elementary plaqu
Externí odkaz:
http://arxiv.org/abs/1204.5521
Autor:
Lobb, S. B., Nijhoff, F. W.
The lattice Gel'fand-Dikii hierarchy was introduced by Nijhoff, Papageorgiou, Capel and Quispel in 1992 as the family of partial difference equations generalizing to higher rank the lattice Korteweg-de Vries systems, and includes in particular the la
Externí odkaz:
http://arxiv.org/abs/0911.1234
Autor:
Spicer, P. E., Nijhoff, F. W.
A semi-discrete Lax pair formed from the differential system and recurrence relation for semi-classical orthogonal polynomials, leads to a discrete integrable equation for a specific semi-classical orthogonal polynomial weight. The main example we us
Externí odkaz:
http://arxiv.org/abs/0907.2158
We present a Lagrangian for the bilinear discrete KP (or Hirota-Miwa) equation. Furthermore, we show that this Lagrangian can be extended to a Lagrangian 3-form when embedded in a higher dimensional lattice, obeying a closure relation. Thus we establ
Externí odkaz:
http://arxiv.org/abs/0906.5282
Autor:
Nijhoff, F. W.
In the paper [V. Adler, IMRN {\bf 1} (1998) 1--4] a lattice version of the Krichever-Novikov equation was constructed. We present in this note its Lax pair and discuss its elliptic form.
Comment: 17 pages, 3 figures
Comment: 17 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/nlin/0110027