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Transformations of Darboux Integrable Systems

, 2009
This article reviews some recent theoretical results about the structure of Darboux integrable differential systems and their relationship with symmetry reduction of exterior differential systems.
Mark E. Fels, Ian M. Anderson, Fels, Mark E., Anderson, Ian M.   +3 more
core   +1 more source

Two-peak soliton in the CKP hierarchy [PDF]

, 2006
We present a systematic approach to the construction of soliton solutions for the 5-reduction of the C-type sub-hierarchy for the Kadomtsev–Petviashvili (CKP) hierarchies starting from the general τ-function τ(n+k) of the Kadomtsev–Petviashvili (KP ...
Cheng, Yi, He, Jingsong, Roemer, Rudolf A.   +2 more
core   +1 more source

Restricted Flows and the Soliton Equation with Self-Consistent Sources

Symmetry, Integrability and Geometry: Methods and Applications, 2006
The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Bäcklund transformation for the restricted flows (by V.B. Kuznetsov et al.
Runliang Lin, Haishen Yao, Yunbo Zeng
doaj  

Double-Step Shape Invariance of Radial Jacobi-Reference Potential and Breakdown of Conventional Rules of Supersymmetric Quantum Mechanics

Axioms
The paper reveals some remarkable form-invariance features of the ‘Jacobi-reference’ canonical Sturm–Liouville equation (CSLE) in the particular case of the density function with the simple pole at the origin.
Gregory Natanson
doaj   +1 more source

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

Two Kinds of Darboux-Bäcklund Transformations for the q-Deformed KdV Hierarchy with Self-Consistent Sources

Advances in Mathematical Physics, 2016
Two kinds of Darboux-Bäcklund transformations (DBTs) are constructed for the q-deformed Nth KdV hierarchy with self-consistent sources (q-NKdVHSCS) by using the q-deformed pseudodifferential operators.
Hongxia Wu, Liangjuan Gao, Jingxin Liu, Yunbo Zeng   +3 more
doaj   +1 more source

Optical Darboux Transformer

Physical Review Letters
The Optical Darboux Transformer is introduced as a photonic device which performs the Darboux transformation directly in the optical domain. This enables two major advances for signal processing based on the nonlinear Fourier transform: (i) the multiplexing of different solitonic waveforms corresponding to arbitrary number of discrete eigenvalues of ...
openaire   +3 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

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
openaire   +3 more sources

Suprathermal Soliton Solutions to Nonlinear Schrödinger Equation

Contributions to Plasma Physics, Volume 66, Issue 3, March 2026.
ABSTRACT Maxwell distributions are very difficult to find in the low‐pressure environment far away the Earth atmosphere, permeated by high temperatures, various types of radiation, highly energetic particles, space debris, and subjected to microgravity, presenting crucial challenges for spacecraft design and operations, and affecting astronaut's health.
F. E. M. Silveira, M. H. Benetti, I. L. Caldas   +2 more
wiley   +1 more source