Results 51 to 60 of about 2,288,345 (293)

Exactly Solvable Time-Dependent Oscillator-Like Potentials Generated by Darboux Transformations [PDF]

, 2017
The stationary Schrödinger equation of the harmonic oscillator is deformed by a Darboux transformation to construct time-dependent potentials with the oscillator profile.
K. Zelaya, O. Rosas‐Ortiz
semanticscholar   +1 more source

Darboux Transformation for the Hirota Equation

Zurnal matematiceskoj fiziki, analiza, geometrii, 2022
The Hirota equation is an integrable higher order nonlinear Schrödinger type equation which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for the Hirota equation and then construct its quasideterminant solutions.
openaire   +5 more sources

Periodic discrete Darboux transforms

Differential Geometry and its Applications, 2023
We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider the integrable reduction to the case of discrete bicycle correspondence.
Joseph Cho, Katrin Leschke, Yuta Ogata
openaire   +3 more sources

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

Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrodinger operator

, 2003
With this paper we begin an investigation of difference schemes that possess Darboux transformations and can be regarded as natural discretizations of elliptic partial differential equations.
A. Doliwa, Ablowitz, Adler, Bogdanov, Doliwa, Doliwa, Doliwa, Dynnikov, Eisenhart, Ernst, Flaschka, Grundland, Hildebrand, Jonas, Konopelchenko, M. Nieszporski, Manakov, Manakov, Manas, Matveev, Misner, Moutard, Nieszporski, Nimmo, Novikov, Novikov, P.M. Santini, Schief, Shabat, Suris, Toda, Veselov   +31 more
core   +1 more source

Reductions of Darboux transformations for the PT-symmetric nonlocal Davey-Stewartson equations

Applied Mathematics Letters, 2018
In this letter, a study of the reductions of the Darboux transformations (DTs) for the PT -symmetric nonlocal Davey–Stewartson (DS) equations is presented. Firstly, a binary DT is constructed in integral form for the PT -symmetric nonlocal DS-I equation.
Bo Yang, Yong Chen
semanticscholar   +1 more source

Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrödinger equation. [PDF]

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants.
Xiaoyong Wen, Yunqing Yang, Zhenya Yan
semanticscholar   +1 more source

D-Modules and Darboux Transformations

Letters in Mathematical Physics, 1998
A method of G. Wilson for generating commutative algebras of ordinary differential operators is extended to higher dimensions. Our construction, based on the theory of D-modules, leads to a new class of examples of commutative rings of partial differential operators with rational spectral varieties.
Berest, Yu., Kasman, A.
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, Adrián Ruiz, Concepción Muriel   +2 more
wiley   +1 more source

Confluent Crum-Darboux transformations in Dirac Hamiltonians with $PT$-symmetric Bragg gratings [PDF]

, 2016
We consider optical systems where propagation of light can be described by a Dirac-like equation with $PT$-symmetric Hamiltonian. In order to construct exactly solvable configurations, we extend the confluent Crum-Darboux transformation for the one ...
F. Correa, V. Jakubský
semanticscholar   +1 more source