Results 41 to 50 of about 452 (186)

A grassmannian version of the darboux transformation

Bulletin des Sciences Mathématiques, 1999
In soliton theory, a Darboux transformation (DT) refers to the following process: First factorize a given second order operator \(L=(d/dx)^2-q\) as a product of two first order operators. Then, swap the order of these operators to obtain a new operator \(\widetilde{L}=(d/dx)^2-\widetilde{q}\).
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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, Volume 49, Issue 9, Page 9814-9831, June 2026.
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

A Five-Component Generalized mKdV Equation and Its Exact Solutions

Mathematics, 2020
In this paper, a 3 × 3 spectral problem is proposed and a five-component equation that consists of two different mKdV equations is derived. A Darboux transformation of the five-component equation is presented relating to the gauge transformations
Bo Xue, Huiling Du, Ruomeng Li
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Probabilistic correlation functions of the Schwarzian field theory

Proceedings of the London Mathematical Society, Volume 132, Issue 6, June 2026.
Abstract We study correlation functions of the probabilistic Schwarzian field theory. We compute cross‐ratio correlation functions exactly in the case when the corresponding Wilson lines do not intersect, confirming predictions made in the physics literature via limit of the conformal bootstrap and the DOZZ formula.
Ilya Losev
wiley   +1 more source

Geometry of Supergravity and the Batalin–Vilkovisky Formulation of the N=1$\mathcal N=1$ Theory in Ten Dimensions

Fortschritte der Physik, Volume 74, Issue 5, May 2026.
ABSTRACT We provide full details of a BV formulation of N=1$\mathcal N=1$ supergravity in 10 dimensions, to all orders in fermions, built from the generalised geometry description of the theory. In contrast to standard treatments, we introduce neither the degrees of freedom corresponding to orthonormal frames for the metric nor the local Lorentz ...
Julian Kupka, Charles Strickland‐Constable, Fridrich Valach   +2 more
wiley   +1 more source

Darboux transformation and solution of the modified Korteweg–de Vries equation

Қарағанды университетінің хабаршысы. Математика сериясы, 2015
Darboux transformation and a comprehensive approach to construct exact solutions of the nonlinear differential equation are counted. It is applied to construct the explicit solutions of the (2+1)-dimensional modified Korteweg-de Vries (KdV) equation. In
G. Kemelbekova, K. Yesmakhanova, S. Tapeeva, D. Tungushbaeva   +3 more
doaj  

Closed Form Relations and Higher‐Order Approximations of First and Second Derivatives of the Tangent Operator on SE(3)

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 4, April 2026.
ABSTRACT The Lie group SE3$SE\left(3\right)$ of isometric orientation‐preserving transformation is used for modeling multibody systems, robots, and Cosserat continua. The use of these models in numerical simulation and optimization schemes necessitates the exponential map, its right‐trivialized differential (often referred to as the tangent operator ...
Andreas Müller
wiley   +1 more source

Soliton Solutions for the Wick-Type Stochastic KP Equation

Abstract and Applied Analysis, 2012
The Wick-type stochastic KP equation is researched. The stochastic single-soliton solutions and stochastic multisoliton solutions are shown by using the Hermite transform and Darboux transformation.
Y. F. Guo, L. M. Ling, D. L. Li
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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

Generalized Algebraic Bargmann–Darboux Transformations [PDF]

International Journal of Modern Physics A, 1997
Algebraic Bargmann and Darboux transformations for equations of a more general form than the Schrödinger ones with an additional functional dependence h(r) in the right-hand side of equations are constructed. The suggested generalized transformations turn into the Bargmann and Darboux transformations for both fixed and variable values of energy and an
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