Results 41 to 50 of about 1,595,275 (210)
Exceptional orthogonal polynomials and the Darboux transformation [PDF]
, 2010 © IOP Publishing Ltd. The research of DGU was supported in part by MICINN-FEDER grant MTM2009- 06973 and CUR-DIUE grant 2009SGR859. The research of NK was supported in part by NSERC grant RGPIN 105490-2004.
Milson, R. +2 more
core +2 more sources
On Geometric Phase Model in the Theory of Curves With Myller Configuration
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this paper, we introduce a linearly polarized light wave in an optical fiber and rotation of the polarization plane through the Frenet‐type frame with Myller configuration. Since the geometric evaluation and interpretations of a polarized light wave are associated with geometric phase, a new type of geometric phase model has been ...
Zehra İşbilir +2 more
wiley +1 more source
DARBOUX TRANSFORMS AND ORTHOGONAL POLYNOMIALS [PDF]
Bulletin of the Korean Mathematical Society, 2002 In [\textit{F. A. Grünbaum} and \textit{L. Haine}, Symmetries and Integrability of Differential Equations, Estérel, 1994, CRM Proc. Lect. Notes 9, 143-154 (1996; Zbl 0865.33008)] the Darboux transform was used to obtain so-called Bochner-Krall orthogonal polynomials which satisfy a higher order (\(>2\)) spectral type differential equation. This Darboux
openaire +1 more source
Land Degradation &Development, Volume 37, Issue 15, Page 10911-10926, September 2026.ABSTRACT The microtopographic characteristics of terrain are modified by soil management and conservation practices, affecting water infiltration, storage, runoff generation, and sediment transport. However, assessing soil microtopography at representative spatial scales remains challenging and time‐consuming.
Jhonatan Spliethoff +5 more
wiley +1 more source
AxiomsWith a specific Darboux transformation, we construct solutions to the sine-Gordon equation. We use both the simple Darboux transformation as well as the multiple Darboux transformation, which enables the obtainment of compact solutions of this equation ...
Pierre Gaillard
doaj +1 more source
Edge Density Expansions for the Classical Gaussian and Laguerre Ensembles
Studies in Applied Mathematics, Volume 157, Issue 3, September 2026.ABSTRACT Recent work of Bornemann has uncovered hitherto hidden integrable structures relating to the asymptotic expansion of quantities at the soft edge of the Gaussian and Laguerre random matrix ensembles. These quantities are spacing distributions and the eigenvalue density, and the findings cover the cases of the three symmetry classes: orthogonal,
Peter J. Forrester +2 more
wiley +1 more source
Discrete Dynamics in Nature and Society, 2012 We find an interesting phenomenon that the discrete system appearing in a reference can be reduced to the old integrable system given by Merola, Ragnisco, and Tu in another reference.
Xianbin Wu, Weiguo Rui, Xiaochun Hong
doaj +1 more source
Characters of Explicit Solutions for a Semidiscrete Integrable Coupled Equation
Advances in Mathematical Physics, 2021 A semidiscrete integrable coupled system is obtained by embedding a free function into the discrete zero-curvature equation. Then, explicit solutions of the first two nontrivial equations in this system are derived directly by the Darboux transformation ...
Qiulan Zhao, Qianqian Yang, Xiangwen Qu
doaj +1 more source
Studies in Applied Mathematics, Volume 157, Issue 3, September 2026.ABSTRACT High‐frequency seismic wave descriptions are essential for fundamental geophysical applications, including earthquake hypocenter location, magnitude estimation, and traveltime–amplitude tomography. These descriptions rely on two coupled PDEs: the eikonal equation (governing traveltimes) and the transport equation (governing amplitudes ...
Ahmet Beyaz +2 more
wiley +1 more source
Journal of Function Spaces, 2017 The rogue wave solutions are discussed for an inhomogeneous fifth-order nonlinear Schrödinger equation, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain. Using the Darboux matrix, the generalized Darboux transformation
N. Song, W. Zhang, P. Wang, Y. K. Xue
doaj +1 more source