Lagrangian 3-form structure for the Darboux system and the KP hierarchy
FW Nijhoff - Letters in Mathematical Physics, 2023 - Springer
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 …
describing orthogonal curvilinear coordinate systems. It has been shown in the past that this …
On non-autonomous differential-difference AKP, BKP and CKP equations
W Fu, FW Nijhoff - Proceedings of the Royal Society A, 2021 - royalsocietypublishing.org
Based on the direct linearization framework of the discrete Kadomtsev–Petviashvili-type
equations presented in the work of Fu & Nijhoff (Fu W, Nijhoff FW. 2017 Direct linearizing …
equations presented in the work of Fu & Nijhoff (Fu W, Nijhoff FW. 2017 Direct linearizing …
A variational perspective on continuum limits of ABS and lattice GD equations
M Vermeeren - SIGMA. Symmetry, Integrability and Geometry: Methods …, 2019 - emis.de
A pluri-Lagrangian structure is an attribute of integrability for lattice equations and for
hierarchies of differential equations. It combines the notion of multi-dimensional consistency …
hierarchies of differential equations. It combines the notion of multi-dimensional consistency …
On reductions of the discrete Kadomtsev--Petviashvili-type equations
The reduction by restricting the spectral parameters $ k $ and $ k'$ on a generic algebraic
curve of degree $\mathcal {N} $ is performed for the discrete AKP, BKP and CKP equations …
curve of degree $\mathcal {N} $ is performed for the discrete AKP, BKP and CKP equations …
On a coupled Kadomtsev–Petviashvili system associated with an elliptic curve
W Fu, FW Nijhoff - Studies in Applied Mathematics, 2022 - Wiley Online Library
Abstract 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 …
proposed by Date, Jimbo, and Miwa J. Phys. Soc. Jpn., 52: 766–771, 1983, is reinvestigated …
The Sylvester Equation and Kadomtsev–Petviashvili System
W Feng, S Zhao - Symmetry, 2022 - mdpi.com
In this paper, we seek connections between the Sylvester equation and Kadomtsev–
Petviashvili system. By introducing Sylvester equation LM are bold, please chekc if bold …
Petviashvili system. By introducing Sylvester equation LM are bold, please chekc if bold …
Elementary introduction to direct linearisation of integrable systems
W Fu, FW Nijhoff - Nonlinear Systems and Their Remarkable …, 2021 - taylorfrancis.com
We give an elementary introduction to the direct linearisation approach of integrable
systems, which provides a unified framework to understand nonlinear discrete and …
systems, which provides a unified framework to understand nonlinear discrete and …
Direct linearisation of the non-commutative Kadomtsev-Petviashvili equations
G Blower, SJA Malham - arXiv preprint arXiv:2412.01686, 2024 - arxiv.org
We prove that the non-commutative Kadomtsev-Petviashvili (KP) equation and
alifted'modified Kadomtsev-Petviashvili (mKP) equation are directly linearisable, and thus …
alifted'modified Kadomtsev-Petviashvili (mKP) equation are directly linearisable, and thus …
The direct linearization scheme with the Lam\'e function: The KP equation and reductions
X Li, Y Sun, D Zhang - arXiv preprint arXiv:2501.06476, 2025 - arxiv.org
The paper starts from establishing an elliptic direct linearization (DL) scheme for the
Kadomtsev-Petviashvili equation. The scheme consists of an integral equation (involving the …
Kadomtsev-Petviashvili equation. The scheme consists of an integral equation (involving the …
[图书][B] Continuum limits of variational systems
M Vermeeren - 2018 - search.proquest.com
In this thesis we examine how to recover continuous systems from discrete systems, ie
differential equations from difference equations. In particular, we are interested in equations …
differential equations from difference equations. In particular, we are interested in equations …