Results 51 to 60 of about 1,762,917 (199)
On the symplectic structures arising in Optics
, 1996 Geometric optics is analysed using the techniques of Presymplectic Geometry. We obtain the symplectic structure of the space of light rays in a medium of a non constant refractive index by reduction from a presymplectic structure, and using adapted ...
Abraham +21 more
core +2 more sources
Integrable discrete nets in Grassmannians
, 2008 We consider discrete nets in Grassmannians $\mathbb{G}^d_r$ which generalize Q-nets (maps $\mathbb{Z}^N\to\mathbb{P}^d$ with planar elementary quadrilaterals) and Darboux nets ($\mathbb{P}^d$-valued maps defined on the edges of $\mathbb{Z}^N$ such that ...
A. Doliwa +10 more
core +1 more source
Curvature Dependent Energy of Surface Curves in Minkowski Space
International Journal of Analysis and Applications, 2018 In this paper, we firstly introduce kinematics properties of the moving particle lying on a surface S. We assume that the particle corresponds to a different type of surface curves such that they are characterized by using the Darboux vector field W in ...
Talat Korpınar +2 more
doaj +2 more sources
The Frenet and Darboux Instantaneous Rotation Vectors of Curves on Time-Like Surface [PDF]
Mathematical and Computational Applications, 1996 In this paper, depending on the Darboux instantaneous rotation vector of a solid perpendicular trihedron in the Minkowski 3-space [...]
UĞURLU, HASAN HÜSEYİN +1 more
openaire +2 more sources
C∞‐Structures for Liénard Equations and New Exact Solutions to a Class of Klein–Gordon Equations
Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 2795-2822, 15 March 2026.ABSTRACT Liénard equations are analyzed using the recent theory of 𝒞∞‐structures. For each Liénard equation, a 𝒞∞‐structure is determined by using a Lie point symmetry and a 𝒞∞‐symmetry. Based on this approach, a novel method for integrating these equations is proposed, which consists in solving sequentially two completely integrable Pfaffian equations.
Beltrán de la Flor +2 more
wiley +1 more source
Darboux theory of integrability for a class of nonautonomous vector fields [PDF]
Journal of Mathematical Physics, 2009 The goal of this paper is to extend the classical Darboux theory of integrability from autonomous polynomial vector fields to a class of nonautonomous vector fields. We also provide sufficient conditions for applying this theory of integrability and we illustrate this theory in several examples.
Llibre Saló, Jaume, Pantazi, Chara
openaire +3 more sources
Scattering theory for difference equations with operator coefficients
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We investigate a class of second‐order difference equations featuring operator‐valued coefficients with the aim of approaching problems of stationary scattering theory. We focus on various compact perturbations of the discrete Laplacian given in a Hilbert space of bi‐infinite square‐summable sequences with entries from a fixed Hilbert space ...
David Sher +3 more
wiley +1 more source
Noncommutative bispectral Darboux transformations
, 2016 We prove a general theorem establishing the bispectrality of noncommutative Darboux transformations. It has a wide range of applications that establish bispectrality of such transformations for differential, difference and q-difference operators with ...
Geiger, Joel +2 more
core +1 more source
Large‐Amplitude Periodic Solutions to the Steady Euler Equations With Piecewise Constant Vorticity
Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.ABSTRACT We consider steady solutions to the incompressible Euler equations in a two‐dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation theory, we rigorously construct curves of solutions that terminate either with stagnation on the interface ...
Alex Doak +3 more
wiley +1 more source
Odd Invariant Semidensity and Divergence-like Operators on an Odd Symplectic Superspace
, 1997 The divergence-like operator on an odd symplectic superspace which acts invariantly on a specially chosen odd vector field is considered. This operator is used to construct an odd invariant semidensity in a geometrically clear way.
Khudaverdian, O. M.
core +2 more sources