Investigation of Exact Solutions of Perturbed Nonlinear Schrödinger's Equation by $\exp\left(-\Phi\left(\xi\right)\right)$-Expansion Method

In this work, dark and singular soliton solutions of the (1[Formula: see text]+[Formula: see text]2)-dimensional chiral nonlinear Schrödinger’s equation are obtained and analyzed dynamically along with graphical depictions. The extraction of these chiral solitons is carried out using two integration tools such as the modified simple equation method and the [Formula: see text]-expansion method. The validity conditions for the existence of these solitons are also retrieved. It is highlighted that the solitons retrieved here are of chiral nature.

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Optical solitons and stability regions of the higher order nonlinear Schrödinger’s equation in an inhomogeneous fiber

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2021-0165 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Nauman Raza ◽

Ahmad Javid ◽

Asma Rashid Butt ◽

Haci Mehmet Baskonus

Keyword(s):

Expansion Method ◽

Variable Coefficients ◽

Wave Number ◽

Schrödinger’S Equation ◽

Optimal Value ◽

The Media ◽

Fifth Order ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Nonlinear Schrödinger’S Equation

Abstract This paper concerns with the integrability of variable coefficient fifth order nonlinear Schrödinger’s equation describing the dynamics of attosecond pulses in inhomogeneous fibers. Variable coefficients incorporate varying dispersion and nonlinearity which are of physical significance in considering the nonuniform boundaries of fibers as well as the inhomogeneities of the media. The well-known exp(−φ(s))-expansion method is used to retrieve singular and periodic solitons with the aid of symbolic computation. The structures of the obtained solutions are discussed along with their existence criteria. Moreover, the modulation instability analysis is carried out to identify the instability regions. A dispersion relation is extracted between wave number and frequency. The optimal value of the frequency is found for the occurrence of the instability. A detailed discussion of the results is also given along with graphics.

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Exact solutions to the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity by using the first integral method

Nonlinear Analysis Modelling and Control ◽

10.15388/na.16.3.14096 ◽

2011 ◽

Vol 16 (3) ◽

pp. 332-339 ◽

Cited By ~ 13

Author(s):

Hossein Moosaei ◽

Mohammad Mirzazadeh ◽

Ahmet Yildirim

Keyword(s):

Exact Solutions ◽

Integral Method ◽

First Integral ◽

First Integral Method ◽

Schrödinger’S Equation ◽

Kerr Law ◽

Kerr Law Nonlinearity ◽

Schrödinger's Equation ◽

Nonlinear Schrodinger’S Equation ◽

Nonlinear Schrödinger’S Equation

The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the first integral method is used to construct exact solutions of the perturbed nonlinear Schrodinger’s equation (NLSE) with Kerr law nonlinearity. It is shown that the proposed method is effective and general.

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