Results 81 to 90 of about 1,134 (216)

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

Dynamical Behavior and Chaotic Nature of M‐Fractional Paraxial Wave Equation With Three Analytical Methods

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
This research work provides a comprehensive investigation of the M‐fractional paraxial wave equation (M‐fPWE) in describing complex optical phenomena in telecommunication systems and nonlinear media, focusing on the dynamical analysis of optical soliton solutions, the impact of M‐fractional parameters, stability, multistability, and the chaotic nature ...
Md. Mamunur Roshid, Mahtab Uddin, Mohammad Safi Ullah, Golam Mostafa, Ashek Ahmed, Shikha Binwal   +5 more
wiley   +1 more source

THE μ–DARBOUX TRANSFORMATION OF MINIMAL SURFACES

, 2019
The classical notion of the Darboux transformation of isothermic surfaces can be generalised to a transformation for conformal immersions. Since a minimal surface is Willmore, we can use the associated C∗–family of flat connections of the harmonic ...
K. Leschke (7749791), K. Moriya (495544)
core   +1 more source

The Delsarte-Darboux type binary transformations, their differential-geometric and operator structure with applications. Part 1 [PDF]

Opuscula Mathematica, 2006
The structure properties of multidimensional Delsarte-Darboux transmutation operators in parametric functional spaces are studied by means of differential-geometric and topological tools.
Yarema A. Prykarpatsky, Anatoliy M. Samoilenko   +1 more
doaj  

Analysis of Bifurcation, Chaos, and Multiplicative White Noise Intensity of the Stochastic Fractional Nonlinear mCGL Model in an Optical Communication System

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
This manuscript studies the stochastic time fraction modified complex Ginzburg–Landau (SFmCGL) model, an essential dynamical nonlinear model for describing the physical nature of how the optical wave soliton behaves and changes over time in a dynamic optical communication system.
Hala Abd-Elmageed, Md. Mamunur Roshid, Shaimaa A. A. Ahmed, Mohamed Abdalla, Yusuf Gurefe   +4 more
wiley   +1 more source

Optical Solitons and Analysis of Chaotic Nature for the Temporal M‐Fractional Yajima–Oikawa Model in Shortwave and Longwave

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study proposes a comprehensive study on fractional soliton solutions and chaotic nature for the temporal M‐fractional Yajima–Oikawa (YO) model in shortwave and longwave regimes. Utilizing the new Jacobian elliptic function method, the optical soliton solutions are examined with diverse categories, including kinky‐periodic wave, kink with bell wave,
Md. Mamunur Roshid, Mrityunjoy Kumar Pandit, Mahtab Uddin, Golam Mostafa, Harun-Or-Roshid, Pramita Mishra   +5 more
wiley   +1 more source

Darboux transformation for two‐level system

Annalen der Physik, 2005
Abstract We develop the Darboux procedure for the case of the two‐level system. In particular, it is demonstrated that one can construct the Darboux intertwining operator that does not violate the specific structure of the equations of the two‐level system, transforming only one real potential into another real potential. We apply the
Bagrov, V., Baldiotti, M., Gitman, D., Shamshutdinova, V.   +3 more
openaire   +3 more sources

Time-dependent Darboux transformation and supersymmetric hierarchy of Fokker-Planck equations

, 2023
A procedure is presented for solving the Fokker-Planck equation with constant diffusion but non-stationary drift. It is based on the correspondence between the Fokker-Planck equation and the non-stationary Schr\"odinger equation.
Ho, Choon-Lin
core   +1 more source

Quasi-Grammian Solutions of the Generalized Coupled Dispersionless Integrable System

Symmetry, Integrability and Geometry: Methods and Applications, 2012
The standard binary Darboux transformation is investigated and is used to obtain quasi-Grammian multisoliton solutions of the generalized coupled dispersionless integrable system.
Bushra Haider, Mahmood-ul Hassan
doaj   +1 more source

Darboux transformation for classical acoustic spectral problem

International Journal of Mathematics and Mathematical Sciences, 2003
We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two by developing a Darboux (Moutard) transformation formalism for this problem.
A. A. Yurova, A. V. Yurov, M. Rudnev
doaj   +1 more source