Abstract
This paper presents an analytic study on optical solitons of a perturbed nonlinear Schr\{o}dinger's equation (NLSE). An integration tool that is the $\exp\left(-\Phi\left(\xi\right\right)$-expansion approach is used to find exact solutions. As a consequence, hyperbolic, trigonometric and rational function solutions are extracted by this approach.
Highlights
The nonlinear Schrödinger’s equation (NLSE) has a central importance in many natural sciences as well as engineering with numerous interpretations and applications concerning eg. nonlinear optics, protein chemistry, plasma physics and fluid dynamics
This paper will consider the perturbed NLSE which governs the dynamics of solitons in negativeindex material with non-Kerr nonlinearity and third-order dispersion, and the dimensionless form of the equation is given by [1, 2]
The last three terms appear in the context of negative-index material [1,2,3,4,5,6]
Summary
The NLSE (nonlinear Schrödinger equation) has a central importance in many natural sciences as well as engineering with numerous interpretations and applications concerning eg. nonlinear optics, protein chemistry, plasma physics and fluid dynamics. Various analytical and numerical methods have been introduced to obtain solutions of nonlinear evolution equations Some of these methods are F-function method [7], exp-function method [8], Hirota’s bilinear method [9], homotopy perturbation method [10], variational iteration method [11, 12], Adomian Pade approximation [13], Lie group method [14], homogeneous balance method [15], inverse scattering transform method [16], Jacobi elliptic expansion method [17], sine-cosine method [18], (G /G)-expansion method [19] and improved tan(Φ(ξ )/2)-expansion method [20].
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