The fractional comparative study of the non-linear directional couplers in non-linear optics

The wave propagation has the significant role in the field of coastal engineering and ocean. In the geographical fields, waves are primary source of environmental process owed to energy conveyance on floating structure. This study aims to investigate the system of cold bosonic atoms in zig-zag optics lattices. The solitonic patterns of the considered model successfully surveyed by using two integrated analytical techniques new extended direct algebraic and expansion method. The exact solutions are presented by rational, trigonometric, hyperbolic and exponential functions. On the basis of solitons, we need to show that which one is more integrated and robust scheme. These solutions will help to understood the dynamics of cold bosonic atoms in zig-zag optical lattices and the several other systems. Three dimensional as well as two dimensional comparison presented for a cold bosonic atoms model solutions which are revealed diagrammatically for appropriate parameters by using Mathematica. This study will help physicists to predict some new hypothesis and theories in the field of mathematical physics.

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“…Asjad et al. ( 2021 ) found interesting fractional soliton wave profiles with the aid of computational algorithm.…”

Section: Introductionmentioning

confidence: 99%

Analysis of propagating wave structures of the cold bosonic atoms in a zig-zag optical lattice via comparison with two different analytical techniques

et al. 2022

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“…In the last two decades, it has been increasingly popular in a variety of sectors of science and engineering (Alawaideh et al, 2020;Al-Oqali et al, 2016;Herzallah and Baleanu, 2014;Herzallah et al, 2011;Jaradat, 2017;Muslih and Baleanu, 2005). Fractional derivatives have been used in a variety of fields, including classical mechanics (Yu and Wang, 2017), scaling phenomena (Cattani et al, 2014), fractal spacetime (He, 2014), dispersion and turbulence (Chen et al, 2013), astrophysics (Abdel-Salam et al, 2020), potential theory (Bogdan and Byczkowski, 2000), viscoelasticity (Novikov and Voitsekhovskii, 2000), electrodynamics (La Nave et al, 2019), optics (Asjad et al, 2021;Gutiérrez-Vega, 2007a;2007b), and thermodynamics (Magomedov et al, 2018). Fractional derivatives research dates back to Leibniz, and it is still going strong today.…”

Section: Introductionmentioning

confidence: 99%

Fractional formulation of Podolsky Lagrangian density

Al-Oqali¹

2022

Int. j. adv. appl. sci.

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Lagrangians which depend on higher-order derivatives appear frequently in many areas of physics. In this paper, we reformulate Podolsky's Lagrangian in fractional form using left-right Riemann-Liouville fractional derivatives. The equations of motion are obtained using the fractional Euler Lagrange equation. In addition, the energy stress tensor and the Hamiltonian are obtained in fractional form from the Lagrangian density. The resulting equations are very similar to those found in classical field theory.

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“…It has many applications in scienti c and engineering disciplines [8]. Moreover, in everyday life, we encounter lots of examples of waves such as a traveling wave along a straight line, the oscillation of strings or an organ pipe, sound waves in the air, and others [9][10][11][12][13][14][15]. e wave vibrates as it passes, and an oscillation travels through the medium by transferring energy based on moving one particle to another with an e ect on the displacement of the medium [16].…”

Section: Introductionmentioning

confidence: 99%

Existence of Solutions of Boundary Value Problem for Nonlinear One-Dimensional Wave Equations by Fixed Point Method

Gusu

Danu

2022

Mathematical Problems in Engineering

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In this article, we investigate the solutions for a class of initial boundary value problems for nonlinear one-dimensional wave equations using a fixed point method. The findings consider initial and boundary data which lead to determining the nature of classes of the nonlinear one-dimensional wave equation. The obtained results indicate the availability of nonnegative solutions which are proved using the method of the fixed point. A new fixed point approach is effective and used as a definitive modeling method to prove the existence of nonnegative solutions for a class of initial boundary value problems based on recent theoretical arguments. The results in this study are considered with examples.

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The fractional comparative study of the non-linear directional couplers in non-linear optics

Cited by 29 publications

References 38 publications

Analysis of propagating wave structures of the cold bosonic atoms in a zig-zag optical lattice via comparison with two different analytical techniques

Analysis of propagating wave structures of the cold bosonic atoms in a zig-zag optical lattice via comparison with two different analytical techniques

Fractional formulation of Podolsky Lagrangian density

Existence of Solutions of Boundary Value Problem for Nonlinear One-Dimensional Wave Equations by Fixed Point Method

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