Abstract
We analytically study the exact solitary wave solutions of the perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index, which describes the propagation of pulses of various types in optical fiber. We apply three efficient and reliable schemes, specifically, the simple equation method, the (G'/G)-expansion method, and the new Kudryashov method. These approaches lead to a range of solitons and other solutions comprising of the bright solitons, dark solitons, singular solitons, periodic, rational, and exponential solutions. These solutions are also presented graphically. Furthermore, all obtained solutions are verified by symbolic computations.
Highlights
The nonlinear Schrödinger (NLS) equation, which is a primary complete integrable nonlinear dispersive partial differential equation (PDE), has been crucial towards establishing a better understanding of a wide variety of systems from atomic physics and nonlinear optics to rogue waves, deep water waves, plasmas, among others [1, 11, 13, 15, 27, 30]
One of the most interesting and stimulating fields of research in the field of engineering and science has been the search for exact soliton solutions to nonlinear models [7, 8, 10, 12, 16, 24, 26, 32]
The study of solitons has a critical role to play in the creation of new theories in the field mathematical physics
Summary
The nonlinear Schrödinger (NLS) equation, which is a primary complete integrable nonlinear dispersive partial differential equation (PDE), has been crucial towards establishing a better understanding of a wide variety of systems from atomic physics and nonlinear optics to rogue waves, deep water waves, plasmas, among others [1, 11, 13, 15, 27, 30]. The critical concept of this paper is to establish the soliton solutions of NLBM equation incorporated with Kudryashov’s in polarization preserving fibers and nonlinear perturbation terms given as [34]. Where m and n are the maximum intensity and power nonlinearity respectively, λk, k = 1, 2, 3, 4, indicate the coefficients of nonlinearity effects, while s is the coefficient of self-steepening term To achieve this aim, we employed three efficient and reliable schemes, explicitly, the simple equation method, the (G /G)-expansion method, and the new Kudryashov method.
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