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From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag
(American Physical Society, 2018-02)
Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these ...
Master equation approach to propagation in nonlinear fibers
(Optical Society of America, 2021-02)
In this Letter, we revisit the quantum theory of propagation in nonlinear fibers. Unlike previous works, we present an effective propagation equation for the reduced density matrix of the complex envelope of the electric ...
Nonlinear Self-Adjoint Classification of a Burgers-KdV Family of Equations
(Hindawi Publishing CorporationNew YorkEUA, 2014)
Optimal Control of Nonlinear Chemical Reactors via an Initial-Value Hamiltonian Problem
(John Wiley & Sons Ltd, 2006-12)
The problem of designing strategies for optimal feedback control of nonlinear processes, specially for regulation and set-point changing, is attacked in this paper. A novel procedure based on the Hamiltonian equations ...
Measuring self-steepening with the photon-conserving nonlinear Schrödinger equation
(Optical Society of America, 2020-08)
We propose an original, simple, and direct method to measure self-steepening (SS) in nonlinear waveguides. Our proposal is based on results derived from the recently introduced photon-conserving nonlinear Schrödinger ...
Stability of abstract non-linear non-autonomous difference-delay equations
(OXFORD UNIV PRESS, 2009)
On S-asymptotically omega-periodic functions and applications
(PERGAMON-ELSEVIER SCIENCE LTDOXFORD, 2012)
Let (X, parallel to . parallel to) be a Banach space and omega is an element of R. A bounded function u is an element of C([0, infinity); X) is called S-asymptotically omega-periodic if lim(t ->infinity)[u(t + omega) - ...
Ultimate boundedness results for solutions of certain third order nonlinear matrix differential equations
(Universidad de Kragujevac, Facultad de CienciasModelación con Ecuaciones DiferencialesKragujevac, Serbia, 2022)
Equation for modeling two-photon absorption in nonlinear waveguides
(Optical Society of America, 2020-06)
We derive a novel propagation equation for optical waveguides that properly accounts for two-photon absorption (TPA). We start from a simple quantum theory of nonlinear fibers allowing for TPA to be included in a straightforward ...