Soliton solutions of the nonlinear Schrödinger equation with the dual power law nonlinearity and resonant nonlinear Schrödinger equation and their modulation instability analysis

In this paper, based on proposed Riccati mapping technique, we investigated the soliton solutions of fourth-order dispersive nonlinear Schrödinger equation with nonlinearity of dual-power law. The various types of solitons solutions involving some parameters are constructed. These soliton solutions can be useful for understanding the physical nature of the waves spread in the dispersive medium. Furthermore, the Modulation Instability (MI) is discussed by standard linear-stability analysis that shows all achieved results are exact and stable. The movements of some achieved results were presented graphically by giving suitable values to parameters that provide easy understanding to the physical phenomenon of this dynamical model. The obtained results show the simplicity and efficiency of the current used approach.

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Modulation instability analysis of the generalized nonlinear Schrödinger equation and its bright, dark and complexiton soliton solutions

Optik ◽

10.1016/j.ijleo.2019.02.027 ◽

2019 ◽

Vol 183 ◽

pp. 381-388 ◽

Cited By ~ 1

Author(s):

Jin-Jin Mao ◽

Shou-Fu Tian ◽

Tian-Tian Zhang ◽

Xing-Jie Yan

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Modulation Instability ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Instability Analysis ◽

Nonlinear Schrödinger ◽

Generalized Nonlinear Schrödinger Equation

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A novel method for new solutions of time fractional (1+2)-dimensional nonlinear Schrödinger equation involving dual-power law nonlinearity

International Journal of Modern Physics B ◽

10.1142/s0217979219502801 ◽

2019 ◽

Vol 33 (24) ◽

pp. 1950280

Author(s):

S. Saha Ray

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Power Law ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Nonlinear Schrodinger Equation ◽

Jacobi Elliptic Function ◽

Nonlinear Schrödinger ◽

Novel Method ◽

Dual Power

In this paper, a novel method has been used to solve time fractional [Formula: see text]-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity. Using the newly-proposed Jacobi elliptic function expansion method, new double periodic, bright and soliton solutions of the aforesaid equation have been obtained. The results show that the proposed method is a convenient, efficient and straightforward technique to devise new soliton solutions of the presently-mentioned equation.

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Optical solitons and modulation instability analysis to the quadratic-cubic nonlinear Schrödinger equation

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2019.1.2 ◽

2018 ◽

Vol 24 (1) ◽

pp. 20-33 ◽

Cited By ~ 3

Author(s):

Mustafa Inc ◽

Aliyu Isa Aliyu ◽

Abdullahi Yusuf ◽

Dumitru Baleanu

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Modulation Instability ◽

Soliton Solutions ◽

Expansion Method ◽

Nonlinear Schrodinger Equation ◽

Integration Scheme ◽

Instability Analysis ◽

Nonlinear Schrödinger

This paper obtains the dark, bright, dark-bright, dark-singular optical and singular soliton solutions to the nonlinear Schrödinger equation with quadratic-cubic nonlinearity (QC-NLSE), which describes the propagation of solitons through optical fibers. The adopted integration scheme is the sine-Gordon expansion method (SGEM). Further more, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis, and the MI gain spectrum is got. Physical interpretations of the acquired results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the PNSE.

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