[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.

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.

Single-mode Optical Fiber, Solitary Wave, Characteristic Coefficient, Implicit Bogning Function, Propagation, Nonlinear Partial Differential Equation

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