International Journal of Modern Physics and Applications
Articles Information
International Journal of Modern Physics and Applications, Vol.5, No.4, Dec. 2019, Pub. Date: Jan. 14, 2020
Solitary Waves and Modification of the Characteristic Coefficients of a Single-mode Optical Fiber
Pages: 60-65 Views: 1197 Downloads: 286
Authors
[01] Jean Roger Bogning, Department of Physics, Higher Teacher Training College, University of Bamenda, Bamenda, Cameroon.
[02] Christian Ngouo Tchinda, Department of Physics, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon; Centre d’Excellence Africain en Technologie de l’Information et de la Télécommunication, The University of Yaoundé I, Yaoundé, Cameroon.
[03] Rodrique Njikue, Department of Physics, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon; Centre d’Excellence Africain en Technologie de l’Information et de la Télécommunication, The University of Yaoundé I, Yaoundé, Cameroon.
Abstract
We study in this article the conditions to be fulfilled by the properties of a single-mode optical fiber so that certain types of waves of our choice and in particular solitary waves propagate there. What guides our thinking in this work starts from the fact that we asked the question of knowing if it is possible to boost a transmission medium and more precisely the optical fiber so as to propagate exactly the type of signal that we wish. We have estimated that such a thing can be possible only by the modification of the constitutive properties of this waveguide. But in nonlinear partial differential equations which describe the dynamics in the waveguides, the properties of materials are embodied by the coefficients of the terms. Thus, the principle of work is to establish the constraint relationships between the scattering, dissipation and nonlinear coefficients for the proposed wave type to propagate in the fiber or simply that the nonlinear partial differential equation that governs the propagation dynamics in a single-mode optical fiber accepts the solution we need. Once these constraint relations are obtained, we rewrite the corresponding nonlinear partial differential equations. The reliability of the results is tested through the study of the propagation of the solutions obtained. The partial differential equations which describe the dynamics of propagation in the support being of Schrödinger type, in order to easily manipulate the necessary calculations, we make use of the Bogning Djeumen-kofané method extended to the implicit functions to obtain the analytical solutions and the Split-step Fourier programming method for numerical study.
Keywords
Single-mode Optical Fiber, Solitary Wave, Characteristic Coefficient, Implicit Bogning Function, Propagation, Nonlinear Partial Differential Equation
References
[01] Zabusky and kruskal 1965 Interaction of “solitons” in a collisionless plasma and the recurrence of the initial states Phys. Rev. Lett, 15 140-143.
[02] Hasegawa A and Tappert F 1973 Transmission of stationary nonlinear optical pulses in dielectric fibers in anomalous dispersion App. Phys. Lett. 23 142-144.
[03] Mollenauer L F, Stolen R F and Gordon J P 1980 Experimental observation of picoseconds pulse narrowing and solitons in optical fibers Phys. Rev. Lett. 45 1095.
[04] Hirota R 1971 Exact solution of the KdV equation for multiple collisions of solitons Phys. Rev. Lett. 27 1192-1194.
[05] G. P. Agrawal, Nonlinear Fibre Optics, Academic Press, 2012.
[06] G. P. Agrawal, Applications of Nonlinear Fibre Optics, Academic Press, 2012.
[07] Bogning J R, 2019, Mathematics for nonlinear physics: Solitary wave in the center of the resolution of dispersive nonlinear partial differential equations (in press), Dorrance Publishing house USA, 2019.
[08] Bogning J R, DjeumenTchaho C Tand Kofané T C, 2012, Construction of the soliton solutions of the Ginzburg-Landau equations by the new Bogning-DjeumenTchaho-Kofané method, PhysicaScripta 85 025013-025018.
[09] Bogning J R, DjeumenTchaho C T andKofané T C, 2012, Generalization of the Bogning- DjeumenTchaho-Kofane Method for the construction of the solitary waves and the survey of the instabilities, Far East J. Dyn. Sys, 20 (2) 2 101-119.
[10] J. Martin, 1963, Cours de mathématiques pour la préparation aux brevets de technicienssupérieur et pour les écolesd’ingénieurs, premiéreédition, Dunod.
[11] Bogning J R, DjeumenTchaho C T and Kofané T C, 2013, Solitary wave solutions of the modified Sasa- Satsuma nonlinear partial differential equation American Journal of Computational and Applied Mathematics, 3 (2) 97-107.
[12] Bogning J R, DjeumenTchaho C T and Kofané T C, 2012, Generalization of the Bogning-DjeumenTchaho-Kofané method for the construction of the solitary waves and the survey of the instabilities, Far East Journal of Dynamical systems, 20 (2) 101-119.
[13] Bogning J R, 2013, Pulse soliton solutions of the modified KdV and Born-Infeld equations, International Journal of Modern Nonlinear Theory and Application2 135-140.
[14] Bogning J R, Porsezian K, FautsoKuiaté G, Omanda H M, 2015, gap solitary pulses induced by the Modulational instability and discrete effects in array of inhomogeneous optical fibers, Physics Journal 1 (3) 216-224.
[15] Bogning J R, 2015, Nth Order Pulse Solitary Wave Solution and Modulational Instability in the Boussinesq, EquationAmerican Journal of Computational and Applied Mathematics, 5 (6) 182-188.
[16] Bogning J R, Sechn 2015 Solutions of the generalized and modified Rosenau-Hyman Equations, Asian Journal of Mathematics and Computer Research, 9 (1) 2395-4205.
[17] Bogning J R, DjeumenTchaho C T and Omanda H M, 2016, Combined solitary wave solutions in higher-order effects optical fibers, British Journal of Mathematics and Computer Science 13 (3) 1-12.
[18] DjeumenTchaho C T, Bogning J R and Kofané T C, 2012, Modulated Soliton Solution of the Modified Kuramoto-Sivashinsky's Equation, American Journal of Computational and Applied Mathematics, 2 (5) 218-224.
[19] DjeumenTchaho C T, Bogning J Rand Kofane T C, 2011, Multi-Soliton solutions of the modified Kuramoto-Sivashinsky’s equation by the BDK method, Far East J. Dyn. Sys., 15 (2) 83-98.
[20] DjeumenTchaho C T, Bogning J R and Kofane T C, 2010, Construction of the analytical solitary wave solutions of modified Kuramoto-Sivashinsky equation by the method of identification of coefficients of the hyperbolic functions, Far East J. Dyn. Sys, 14 (1) 14-17.
[21] Bogning J R, FautsoKuiaté G, Omanda H M and DjeumenTchaho C T, 2015, Combined Peakons and multiple-peak solutions of the Camassa-Holm and modified KdV equations and their conditions of obtention, Physics Journal, 1 (3) 367-374.
[22] Bogning J R, 2013, Analytical soliton solutions and wave solutions of discrete nonlinear cubic-quintiqueGinzburg-Landau equations in array of dissipative optical system,. American Journal of Computational and Applied Mathematics, 3 (2) 97-105.
[23] Njikue R, Bogning J R and Kofane T C, 2018, Exact bright and dark solitary wave solutions of the generalized higher order nonlinear Schrödinger equation describing the propagation of ultra-short pulse in optical fiber, J. Phys. Commun, 2 025030.
[24] Bogning J R and Kofané T C, 2006, Solitons and dynamics of nonlinear excitations in the array of optical fibers, Chaos, Solitons& Fractals; 27 (2) 377-385.
[25] Bogning J R and Kofané T C, 2006, Analytical solutions of the discrete nonlinear Schrödinger equation in arrays of optical fibers, Chaos, Solitons& Fractals 28 (1) 148-153.
[26] Bogning J R, 2018, Exact solitary wave solutions of the (3+1) modified B-type Kadomtsev-Petviashvili family equations, American Journal of computational and applied mathematics, 8 (5) 85-92.
[27] TiagueTakongmo Guy and Bogning J R, 2018, Construction of solitary wave solutions of higher-order nonlinear partial differential equations modeled in a nonlinear hybrid electrical line, American Journal of circuits, systems and signal processing 4 (3) 36-44.
[28] TiagueTakongmo Guy and Bogning J R, 2018, Construction of solitary wave solutions of higher-order nonlinear partial differential equations modeled in a modified nonlinear Noguchi electrical line, American Journal of circuits, systems and signal processing 4 (1) 8-14.
[29] TiagueTakongmo Guy and Bogning J R, 2018, Construction of solitary wave solutions of higher-order nonlinear partial differential equations modeled in a nonlinear capacitive electrical line, American Journal of circuits, systems and signal processing 4 (2) 15-22.
[30] TiagueTakongmo Guy and Bogning J R, 2018, Construction of solutions in the shape (pulse, pulse) and (kink, kink) of a set of two equations modeled in a nonlinear inductiveelectrical line with crosslink capacitor, American Journal of circuits, systems and signal processing 4 (2) 28-35.
[31] TiagueTakongmo Guy and Bogning J R, 2018,(kink, kink) and (pulse, pulse) exact solutions of equations modeled in a nonlinear capacitive electrical line with capacitor, American Journal of circuits, systems and signal processing 4 (3) 45-53.
[32] TiagueTakongmo Guy and Bogning J R, 2018, Solitary wave solutions of modified telegraphist equations modeled in an electrical line, Physics Journal, 4 (3) 29-36
[33] TiagueTakongmo Guy and Bogning J R, 2018, Coupled solitonsolutionsof modeled equations in a Noguchi electrical line with crosslink capacitor, Journal of Physics communications, 2, 105016.
[34] RodriqueNjikue and Bogning J R, Kofané T C, 2018, higher order nonlinear Schrödinger equation family in optical fiber and solitary wave solutions, American journal of optics, American Journal of optics and photonics 6 (3) 31-41.
[35] Jean Roger Bogning, 2019 Mathematics for nonlinear Physics: solitary waves in the center of resolution of dispersive nonlinear partial differential equations, Dorrance Publishing Co, USA.
[36] Jean Roger Bogning, 2019 Mathematics for Physics: The implicit Bogning functions and applications, Lambert Academic Publishing, Germany.
[37] Ryan Napoleon Foster, 2007, Web based interface for numerical simulations of nonlinear evolution equations.
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