Results 41 to 50 of about 11,987 (207)

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
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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

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

New Exactly Solvable Isospectral Partners for PT Symmetric Potentials

, 2003
We examine in detail the possibilty of applying Darboux transformation to non Hermitian hamiltonians. In particular we propose a simple method of constructing exactly solvable PT symmetric potentials by applying Darboux transformation to higher states of
Abramowitz M, Anjana Sinha, Bender C M, Bender C M, Lévai G, Matveev V B, Pinaki Roy, Robnik M, Znojil M, Znojil M   +9 more
core   +1 more source

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source

Darboux transformation and multi-soliton solutions of Two-Boson hierarchy

, 2010
We study Darboux transformations for the two boson (TB) hierarchy both in the scalar as well as in the matrix descriptions of the linear equation. While Darboux transformations have been extensively studied for integrable models based on $SL(2,R)$ within
Ablowitz M. J., ASHOK DAS, Darboux G., Dodd R. K., Drinfeld V. G., Lamb G. L., U. SALEEM   +6 more
core   +1 more source

Differential Calculi on Associative Algebras and Integrable Systems

, 2020
After an introduction to some aspects of bidifferential calculus on associative algebras, we focus on the notion of a "symmetry" of a generalized zero curvature equation and derive Backlund and (forward, backward and binary) Darboux transformations from ...
A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Sitarz, C Rogers, D-J Zhang, E Brezin, F Magri, F Magri, G Chavchanidze, G Tondo, J Grifone, J Hietarinta, JT Hartwig, LJ Mason, M Crampin, M Crampin, O Chvartatskyi, P Lorenzoni, P Lorenzoni, VA Marchenko, VK Mel’nikov, Y Kosmann-Schwarzbach   +30 more
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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

Solutions to the Sine-Gordon Equation: From Darboux Transformations to Wronskian Representations of the k-Negaton-l-Positon-n-Soliton Solutions

Axioms
With 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

Generalized Darboux transformations for the KP equation with self-consistent sources

, 2004
The KP equation with self-consistent sources (KPESCS) is treated in the framework of the constrained KP equation. This offers a natural way to obtain the Lax representation for the KPESCS.
Ablowitz M J, Cheng Y, Cheng Y, Date E, Deng S F, Dickey L A, Dickey L A, Doktorov E V, Leon J, Matveev V B, Mel'nikov V K, Mel'nikov V K, Mel'nikov V K, Mel'nikov V K, Mel'nikov V K, Oevel W, Ohta Y, Sidorenko J, Ting Xiao, Ye S, Yunbo Zeng, Zeng Y B, Zeng Y B   +22 more
core   +2 more sources