Abstract
In this paper, we modify with an appropriate analytical technique, the characteristics of the optical fiber through the modification of the coefficients of the highly nonlinear partial differential equation, which initially governs the dynamics of the propagation in such a wave guide. The procedure consists to assign arbitrary coefficients to the various terms of the established nonlinear partial differential equation, such as the one that embodies the propagation dynamics in a strongly nonlinear optical fiber and subsequently establishing the constraint equations linking these coefficients and thus the analys is makes it possible to enumerate the criteria for which obtaining the desired solutions is possible. These coefficients are like indicators which characterize the various modifications made in this medium of transmission. The nonlinear evolution equation that served as mathematical model for this study is the higher-order nonlinear Schrodinger equation which better describes the propagation of an ultrafast pulse in an optical fiber. The use of the Bogning-Djeumen Tchaho-Kofane method enabled not only to establish the constraint relations, but also the solitary wave solutions and plane wave solutions. We want through the results obtained in this article to give the specialists of the manufacture of transmission media such as optical fiber, to consider the modification of the properties of this wave guide during manufacture, depending on the type of signal that one wants to propagate in this case notably the solitary wave.
Highlights
Nonlinear Schrodinger (NLS) equation is one of the most interesting nonlinear evolution equation (NEE) used to model phenomena in many area of physics in which nonlinear optics, plasma physics, condensed matter physics, nonlinear quantum field theory, bio-physics and hydrodynamic [1-8]
Rodrique Njikue et al.: Higher-Order Nonlinear Schrödinger Equation Family in Optical Fiber and Solitary Wave Solutions using NEEs, another thing is to construct their exact solutions. The survey of these exact solutions of nonlinear evolution equations has a great importance in the study of nonlinear phenomena
Step[4]: For m = n = 0, and q = r, we look for the values of r which can make some terms of Eq(9) merge
Summary
Nonlinear Schrodinger (NLS) equation is one of the most interesting nonlinear evolution equation (NEE) used to model phenomena in many area of physics in which nonlinear optics, plasma physics, condensed matter physics, nonlinear quantum field theory, bio-physics and hydrodynamic [1-8]. In nonlinear optics, the propagation of picoseconds pulse in monomode fibers is governed by the well-known NLS equation. This equation is known to be integrable and admits bright and dark soliton solutions in anomalous dispersion region and normal dispersion regime respectively [9-10]. The governing equation of the femtosecond pulse propagation in monomode fibers is the Higher-order Nonlinear Schrödinger (HNLS) equation [13]. Rodrique Njikue et al.: Higher-Order Nonlinear Schrödinger Equation Family in Optical Fiber and Solitary Wave Solutions using NEEs, another thing is to construct their exact solutions. The survey of these exact solutions of nonlinear evolution equations has a great importance in the study of nonlinear phenomena. A brief presentation of the novel BDKm is important for the calculations made
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