Results 91 to 100 of about 1,619,181 (215)

Integrable discretization of the vector/matrix nonlinear Schr\"odinger equation and the associated Yang-Baxter map

, 2015
The action of a B\"acklund-Darboux transformation on a spectral problem associated with a known integrable system can define a new discrete spectral problem.
Tsuchida, Takayuki
core  

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, Evripidou, Charalambos, McLaren, David, Owren, Brynjulf, Quispel, Reinout, Tapley, Benjamin   +5 more
core  

On the isoperimetric Riemannian Penrose inequality

Communications on Pure and Applied Mathematics, Volume 78, Issue 5, Page 1042-1085, May 2025.
Abstract We prove that the Riemannian Penrose inequality holds for asymptotically flat 3‐manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the ADM$\operatorname{ADM}$ mass being a well‐defined geometric invariant.
Luca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri   +2 more
wiley   +1 more source

Foundations of Ghost Stability

Fortschritte der Physik, Volume 73, Issue 4, April 2025.
Abstract The authors present a new method to analytically prove global stability in ghost‐ridden dynamical systems. The proposal encompasses all prior results and consequentially extends them. In particular, it is shown that stability can follow from a conserved quantity that is unbounded from below, contrary to expectation.
Verónica Errasti Díez, Jordi Gaset Rifà, Georgina Staudt   +2 more
wiley   +1 more source

Nondensity results in high‐dimensional stable Hamiltonian topology

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract We push forward the study of higher dimensional stable Hamiltonian topology by establishing two nondensity results. First, we prove that stable hypersurfaces are not C3$C^3$‐dense in any isotopy class of embedded hypersurfaces on any ambient symplectic manifold of dimension 2n⩾8$2n\geqslant 8$.
Robert Cardona, Fabio Gironella
wiley   +1 more source

Lagrangian approximation of totally real concordances

Proceedings of the London Mathematical Society, Volume 130, Issue 4, April 2025.
Abstract We show that a two‐dimensional totally real concordance can be approximated by a Lagrangian concordance whose Legendrian boundary has been stabilised both positively and negatively sufficiently many times. The main applications that we provide are constructions of knotted Lagrangian concordances in arbitrary four‐dimensional symplectisations ...
Georgios Dimitroglou Rizell
wiley   +1 more source

On the Special Viviani’s Curve and Its Corresponding Smarandache Curves

Mathematics
In the present paper, the special Viviani’s curve is revisited in the context of Smarandache geometry. Accordingly, the paper first defines the special Smarandache curves of Viviani’s curve, including the Darboux vector.
Yangke Deng, Yanlin Li, Süleyman Şenyurt, Davut Canlı, İremnur Gürler   +4 more
doaj   +1 more source

Darboux integrals for Schrödinger planar vector fields via Darboux transformations

, 2011
In this paper we study the Darboux transformations of planar vector fields of Schrödinger type. Using the isogaloisian property of Darboux transformation we prove the “invariance” of the elements of the “Darboux Theory of Integrability”. In particular, we also show how the shape invariance property of the potential is important in order to preserve the
Acosta Humánez, Primitivo Belén, Pantazi, Chara   +1 more
openaire   +1 more source

Geometric B\"acklund--Darboux transformations for the KP hierarchy

, 1998
We shown that, if you have two planes in the Segal-Wilson Grassmannian that have an intersection of finite codimension, then the corresponding solutions of the KP hierarchy are linked by B\"acklund-Darboux transformations (BDT).
Helminck, G. F., van de Leur, J. W.
core  

CHARACTERIZATIONS OF SPACE CURVES WITH 1-TYPE DARBOUX INSTANTANEOUS ROTATION VECTOR

Communications of the Korean Mathematical Society, 2016
Abstract. In this study, by using Laplace and normal Laplace operators,we give some characterizations for the Darboux instantaneous rotationvector field of the curves in the Euclidean 3-space E 3 . Further, we givenecessary and sufficient conditions for unit speed space curves to have1-type Darboux vectors.
ARSLAN, KADRİ, Onder, Mehmet, Kocayigit, Huseyin   +2 more
openaire   +3 more sources