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Selective Impact of Dispersion and Nonlinearity on Waves and Solitary Wave in a Strongly Nonlinear and Flattened Waveguide

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Open Journal of Applied Sciences 2024年第7期14卷 1730-1753页

作者： Christian Regis Ngouo Tchinda marcelle nina zambo abou’ou Jean Roger Bogning Department of Physics Faculty of Science University of Yaound I Yaound Cameroon Centre dExcellence Africain en Technologie de lInformation et de la Tlcommunication The University of Yaound I Yaound Cameroon African Optical Fiber Family Bafoussam Cameroon Department of Physics Faculty of Science University of Bamenda Bamenda Cameroon Department of Physics Higher Teacher Training College University of Bamenda Bamenda Cameroon

The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide contains multiple dispersion coefficients according to the degrees of spatial variation within it, our work in this article is to see how these dispersions and nonlinearities each influence the wave or the signal that can propagate in the waveguide. Since the partial differential equation which governs the dynamics of propagation in such transmission medium presents several dispersion and nonlinear coefficients, we check how they contribute to the choices of the solutions that we want them to verify this nonlinear partial differential equation. This effectively requires an adequate choice of the form of solution to be constructed. Thus, this article is based on three main pillars, namely: first of all, making a good choice of the solution function to be constructed, secondly, determining the exact solutions and, if necessary, remodeling the main equation such that it is possible;then check the impact of the dispersion and nonlinear coefficients on the solutions. Finally, the reliability of the solutions obtained is tested by a study of the propagation. Another very important aspect is the use of notions of probability to select the predominant solutions.

关键词： Flattened Waveguide Solitary Wave Characteristic Coefficient Probabilities Propagation Nonlinear Dispersive Partial Differential Equation

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Influence of Waveguide Properties on Wave Prototypes Likely to Accompany the Dynamics of Four-Wave Mixing in Optical Fibers

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Journal of Applied Mathematics and Physics 2024年第7期12卷 2601-2633页

作者： Jean Roger Bogning marcelle nina zambo abou’ou Christian Regis Ngouo Tchinda Mathurin Fomekong Oriel Loh Ndichia Stallone Mezezem Songna François Béceau Pelap Department of Physics Higher Teacher Training College University of Bamenda Bamenda Cameroon African Optical Fiber Family Bafoussam Cameroon Department of Physics Faculty of Science University of Bamenda Bamenda Cameroon Department of Physics Faculty of Science University of Yaound I Yaound Cameroon Africain en Technologie de lInformation et de la Tlcommunication The University of Yaound I Yaound Cameroon Unit de Recherche de Mcanique et de Modlisation des Systmes Physiques (UR-2MSP) Facult des Sciences Universit de Dschang Dschang Cameroun

In this article, we study the impacts of nonlinearity and dispersion on signals likely to propagate in the context of the dynamics of four-wave mixing. Thus, we use an indirect resolution technique based on the use of the iB-function to first decouple the nonlinear partial differential equations that govern the propagation dynamics in this case, and subsequently solve them to propose some prototype solutions. These analytical solutions have been obtained;we check the impact of nonlinearity and dispersion. The interest of this work lies not only in the resolution of the partial differential equations that govern the dynamics of wave propagation in this case since these equations not at all easy to integrate analytically and their analytical solutions are very rare, in other words, we propose analytically the solutions of the nonlinear coupled partial differential equations which govern the dynamics of four-wave mixing in optical fibers. Beyond the physical interest of this work, there is also an appreciable mathematical interest.

关键词： Optical Fiber Four Waves Mixing Implicit Bogning Function Coupled Nonlinear Partial Differential Equations Nonlinear Coefficient Dispersive Coefficient Waveguide Properties

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