Abstract
With the increasing input power in optical fibers, the dispersion problem is becoming a severe restriction on wavelength division multiplexing (WDM). With the aid of solitons, in which the shape and speed can remain constant during propagation, it is expected that the transmission of nonlinear ultrashort pulses in optical fibers can effectively control the dispersion. The propagation of a nonlinear ultrashort laser pulse in an optical fiber, which fits the high-order nonlinear Schrödinger equation (NLSE), has been solved using the G'/G expansion method. Group velocity dispersion, self-phase modulation, the fourth-order dispersion, and the fifth-order nonlinearity of the high-order NLSE were taken into consideration. A series of solutions has been obtained such as the solitary wave solutions of kink, inverse kink, the tangent trigonometric function, and the cotangent trigonometric function. The results have shown that the G'/G expansion method is an effective way to obtain the exact solutions for the high-order NLSE, and it provides a theoretical basis for the transmission of ultrashort pulses in nonlinear optical fibers.
Highlights
It is understood that a soliton is excited by a nonlinear field, and its energy is relatively concentrated in a small area
A good understanding of the G/G expansion method is of great significance to the transmission application of ultrashort pulses in nonlinear optical fibers
This paper presents the method in detail with examples for obtaining multiple soliton solutions
Summary
It is understood that a soliton is excited by a nonlinear field, and its energy is relatively concentrated in a small area. After rigorous theoretical and mathematical deduction, he predicted that both bright and dark soliton pulses were present in an optical fiber. He proved that any nondestructive optical pulse could travel as stable as a soliton during its transmission in an optical fiber. The G/G expansion method [4], one of the methods for obtaining exact solutions for NLSE, has attracted much attention recently [4,5,6]. It plays an important role in deriving the propagation wave solution of NLSE. This paper presents the method in detail with examples for obtaining multiple soliton solutions
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