Results 61 to 70 of about 6,078 (188)
Darboux transformations for a Bogoyavlenskii equation in 2+1 dimensions
, 1999 We use the singular manifold method to obtain the Lax pair, Darboux transformations and soliton solutions for a (2+1) dimensional integrable equation.Comment: 7 pages, latex, to appear in the proceedings of the meeting "Nonlinearity and Integrability" (
Estevez, P. G., Hernaez, G. A.
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Exact Solution of the Nonlocal
MathematicsThis paper investigates the (2 + 1)-dimensional nonlocal Hirota–Maxwell–Bloch (NH-MB) system under various types of nonlocality. The mathematical consistency of possible nonlocal structures is analyzed, and three types that lead to a well-posed system ...
Zhaidary Myrzakulova +3 more
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Bäcklund transformations for Darboux integrable differential systems [PDF]
Selecta Mathematica, 2014 61 ...
Anderson, I. M., Fels, M. E.
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International Journal for Numerical Methods in Engineering, Volume 126, Issue 23, 15 December 2025.ABSTRACT We apply the discrete mechanics approach to the discretisation of geometrically exact Cosserat rods. We consider discrete Cosserat rods defined on a vertex (or nodal) grid, as well as on a staggered grid, and provide a review and update of the results already obtained in Part I for the nodal model variant and, for the first time, present a ...
Holger Lang +5 more
wiley +1 more source
Darboux Transformations in Integrable Systems [PDF]
, 2005 The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry.
Chaohao Gu, Hesheng Hu, Zixiang Zhou
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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 +2 more
wiley +1 more source
, 2007 An integrable self-adjoint 7-point scheme on the triangular lattice and an integrable self-adjoint scheme on the honeycomb lattice are studied using the sublattice approach.
A. Doliwa +6 more
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Pseudo-abelian integrals on slow-fast Darboux systems [PDF]
Annales de l'Institut Fourier, 2013 We study pseudo-abelian integrals associated with polynomial deformations of slow-fast Darboux integrable systems. Under some assumptions we prove local boundedness of the number of their zeros.
Bobieński, Marcin +2 more
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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 +3 more
wiley +1 more source
Detecting and determining preserved measures and integrals of rational maps
, 2020 In this paper we use the method of discrete Darboux polynomials to calculate preserved measures and integrals of rational maps. The approach is based on the use of cofactors and Darboux polynomials and relies on the use of symbolic algebra tools.
Celledoni, Elena +5 more
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