Results 61 to 70 of about 9,686 (209)

Darboux-type transformations and hyperelliptic curves [PDF]

Journal für die reine und angewandte Mathematik (Crelles Journal), 2000
We systematically study Darboux-type transformations for the KdV and AKNS hierarchies and provide a complete account of their effects on hyperelliptic curves associated with algebro-geometric solutions of these hierarchies.
Gesztesy, Fritz, Holden, Helge
openaire   +3 more sources

Numerical and Analytical Investigation of the Ablowitz–Ladik and Salerno Models: Closeness to Cubic and Cubic‐Quintic Discrete Nonlinear Schrödinger Lattices

Studies in Applied Mathematics, Volume 155, Issue 6, December 2025.
ABSTRACT We study the closeness between the Ablowitz–Ladik, Salerno, and discrete nonlinear Schrödinger lattices in regimes of small coupling ε$\varepsilon$ and small energy norm ρ$\rho$. Two approaches are compared: direct estimates in physical variables and a transformation to canonical symplectic coordinates via Darboux variables.
Marco Calabrese, Tiziano Penati, Simone Paleari   +2 more
wiley   +1 more source

Darboux and binary Darboux transformations for discrete integrable systems 1. Discrete potential KdV equation

, 2013
The Hirota-Miwa equation can be written in `nonlinear' form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation.
Nimmo, Jonathan J C, Shi, Ying, Zhang, Da-jun   +2 more
core   +1 more source

A Method for Obtaining Darboux Transformations [PDF]

Journal of Nonlinear Mathematical Physics, 1998
In this paper we give a method to obtain Darboux transformations (DTs) of integrable equations. As an example we give a DT of the dispersive water wave equation. Using the Miura map, we also obtain the DT of the Jaulent-Miodek equation. \end{abstract}
Lu, Baoqun, He, Yong, Ni, Guangjiong
openaire   +2 more sources

Floer theory for the variation operator of an isolated singularity

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analog for an isolated singularity. We define the monodromy Lagrangian Floer cohomology, which provides categorifications of the standard theorems on the variation operator and the ...
Hanwool Bae, Cheol‐Hyun Cho, Dongwook Choa, Wonbo Jeong   +3 more
wiley   +1 more source

Darboux transformation of symmetric Jacobi matrices and Toda lattices

Frontiers in Applied Mathematics and Statistics
Let J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively.
Ivan Kovalyov, Oleksandra Levina
doaj   +1 more source

Lattice and q-difference Darboux-Zakharov-Manakov systems via $\bar{\partial}$-dressing method

, 1995
A general scheme is proposed for introduction of lattice and q-difference variables to integrable hierarchies in frame of $\bar{\partial}$-dressing method .
B G Konopelchenko, Bianchi L, Bogdanov L V, Bogdanov L V, Bogdanov L V, Carroll R, Darboux G, Dryuma V S, Dryuma V S, Dubrovin B, Dubrovin B, Dubrovin B A, Eisenhart L P, Forsyth A R, Konopelchenko B G, Konopelchenko B G, L V Bogdanov, Nijhoff F, Schief W K, Tsarev S P, Tsarev S P, Zakharov V E, Zakharov V E, Zakharov V E   +23 more
core   +1 more source

One-parameter Darboux-transformed quantum actions in Thermodynamics [PDF]

, 2001
We use nonrelativistic supersymmetry, mainly Darboux transformations of the general (one-parameter) type, for the quantum oscillator thermodynamic actions.
Arnaud J, Boya L J, Fermin Aceves de la Cruz, Haret C Rosu, Rosu H C, Zwillinger D   +5 more
core   +4 more sources

Darboux transformation with dihedral reduction group [PDF]

Journal of Mathematical Physics, 2014
We construct the Darboux transformation with Dihedral reduction group for the 2-dimensional generalisation of the periodic Volterra lattice. The resulting Bäcklund transformation can be viewed as a nonevolutionary integrable differential difference equation. We also find its generalised symmetry and the Lax representation for this symmetry.
Mikhailov, Alexander V, Papamikos, Georgios, Wang, Jing Ping   +2 more
openaire   +4 more sources

Existence and orthogonality of stable envelopes for bow varieties

Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3249-3306, November 2025.
Abstract Stable envelopes, introduced by Maulik and Okounkov, provide a family of bases for the equivariant cohomology of symplectic resolutions. They are part of a fascinating interplay between geometry, combinatorics and integrable systems. In this expository article, we give a self‐contained introduction to cohomological stable envelopes of type A$A$
Catharina Stroppel, Till Wehrhan
wiley   +1 more source