Results 1 to 10 of about 1,170,323 (284)

Application of the unified method to solve the ion sound and Langmuir waves model

Heliyon, 2022
We present the unified method and use it to integrate the ion sound and Langmuir waves (ISLW) model to retrieve optical soliton solutions. Some new dynamical optical solitons involving the combo of rational, trigonometric, and hyperbolic function ...
Dulal Chandra Nandi, Mohammad Safi Ullah, Harun-Or- Roshid, M. Zulfikar Ali   +3 more
doaj   +4 more sources

The Unified Method: III Non-Linearizable Problems on the Interval [PDF]

Journal of Physics A: Mathematical and Theoretical, 2011
Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and used extensively in the literature.
A S Fokas, Fokas A S, Fokas A S, J Lenells, Lenells J   +4 more
core   +2 more sources

The Unified Method: I Non-Linearizable Problems on the Half-Line [PDF]

Journal of Physics A: Mathematical and Theoretical, 2011
Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature.
A S Fokas, Bikbaev R F, Bona J L, Boutet de Monvel A, Coddington E A, Deconinck B Trogdon T Vasan V, Doschoris M, Fokas A S, Fokas A S, Fokas A S, Fokas A S, Fokas A S, Fokas A S, Fokas A S, Fokas A S Pelloni B, Habibullin I T, Its A R, J Lenells, Lenells J, Lenells J, Lenells J, Lenells J, Pelloni B, Smith D A, Smith D A, Tarasov V O, Vetra S   +26 more
core   +2 more sources

Laplace's equation on convex polyhedra via the unified method. [PDF]

Proc Math Phys Eng Sci, 2015
We provide a new method to study the classical Dirichlet problem for Laplace's equation on a convex polyhedron. This new approach was motivated by Fokas’ unified method for boundary value problems. The central object in this approach is the global relation: an integral equation which couples the known boundary data and the unknown boundary values. This
Ashton AC.
europepmc   +4 more sources

The projection method: a unified formalism for community detection

Frontiers in Complex Systems
We present the class of projection methods for community detection that generalizes many popular community detection methods. In this framework, we represent each clustering (partition) by a vector on a high-dimensional hypersphere. A community detection
Martijn Gösgens, Remco van der Hofstad, Nelly Litvak   +2 more
doaj   +4 more sources

Dynamic Properties of Non-Autonomous Femtosecond Waves Modeled by the Generalized Derivative NLSE with Variable Coefficients

Crystals, 2022
The primary purpose of this study is to analyze non-autonomous femtosecond waves with various geometrical configurations correlated to the generalized derivative nonlinear Shrödinger equation (NLSE) with variable coefficients.
Mohamed Adel, Khaled Aldwoah, Farrie Alharbi, Mohamed S. Osman   +3 more
doaj   +1 more source

Distinct exact solutions for the conformable fractional derivative Gerdjikov-Ivanov equation via three credible methods

Journal of Taibah University for Science, 2023
This paper reveals the conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation, which is applied to nonlinear fibre optics together with photonic crystal fibres.
Qinglian Yin, Ben Gao, Zhang Shi
doaj   +1 more source

A new study of soliton solutions for the variable coefficients Caudrey–Dodd–Gibbon equation

Journal of Taibah University for Science, 2022
We present a paper on the different methods for finding solutions to the Caudrey–Dodd–Gibbon equation with variable coefficients, which has wide applications in quantum mechanics and nonlinear optics.
Qinglian Yin, Ben Gao
doaj   +1 more source

Unveiling parametric effects on optical solitons of the Phi-4 model in mathematical physics

Partial Differential Equations in Applied Mathematics, 2023
In the intricate realms of quantum field theory, cosmology, and condensed matter physics, the Phi-4 model emerges as a potent catalyst, shaping mathematical landscapes with profound implications. Our research has uncovered a set of soliton solutions that
Md. Abde Mannaf, Rajandra Chadra Bhowmik, Mst. Tania Khatun, Md. Ekramul Islam, Udoy S. Basak, M. Ali Akbar   +5 more
doaj   +1 more source

CUE: The continuous unified electronic diary method [PDF]

Behavior Research Methods, 2012
In the present article, we introduce the continuous unified electronic (CUE) diary method, a longitudinal, event-based, electronic parent report method that allows real-time recording of infant and child behavior in natural contexts. Thirty-nine expectant mothers were trained to identify and record target behaviors into programmed handheld computers ...
Ellis-Davies, K., Sakkalou, E., Fowler, N., Hilbrink, E., Gattis, M.   +4 more
openaire   +3 more sources