New exact solutions for the Wick-type stochastic nonlinear Schrödinger equation in nonlinear optics

2019 ◽  
Vol 33 (09) ◽  
pp. 1950109 ◽  
Author(s):  
S. Singh ◽  
S. Saha Ray
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Auxiliary Equation ◽  
Auxiliary Equation Method ◽  
Hermite Transform ◽  
Nonlinear Schrödinger ◽  
New Exact Solutions

The exact solutions of Wick-type stochastic nonlinear Schrödinger equation (NLSE) using extended auxiliary equation method (EAEM) has been obtained in this paper. Hermite transform has been used for transforming the stochastic NLSE into deterministic PDE. Also, the stochastic solutions in the white noise space have been obtained by applying inverse Hermite transform on the deterministic set of solutions.

New optical soliton solutions of fractional perturbed nonlinear Schrödinger equation in nanofibers

2021 ◽  
Author(s):  
S. Saha Ray ◽  
N. Das
Keyword(s):  
Differential Equation ◽  
Schrödinger Equation ◽  
Differential Equations ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
New Exact Solutions

In this article, the space-time fractional perturbed nonlinear Schrödinger equation (NLSE) in nanofibers is studied using the improved [Formula: see text] expansion method (ITEM) to explore new exact solutions. The perturbed nonlinear Schrodinger equation is a nonlinear model that occurs in nanofibers. The ITEM is an efficient method to obtain the exact solutions for nonlinear differential equations. With the help of the modified Riemann–Liouville derivative, an equivalent ordinary differential equation has been obtained from the nonlinear fractional differential equation. Several new exact solutions to the fractional perturbed NLSE have been devised using the ITEM, which is the latest proficient method for analyzing nonlinear partial differential models. The proposed method may be applied for searching exact travelling wave solutions of other nonlinear fractional partial differential equations that appear in engineering and physics fields. Furthermore, the obtained soliton solutions are depicted in some 3D graphs to observe the behaviour of these solutions.

New Analytical Solutions to the Nonlinear Schrödinger Equation Model

2005 ◽  
Vol 60 (11-12) ◽  
pp. 775-782 ◽  
Author(s):  
Yuanyuan Zhang ◽  
Ying Zheng ◽  
Hongqing Zhang
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Equation Model ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
New Exact Solutions

In this paper, new analytical solutions of the nonlinear Schrödinger equation model are obtained. The properties of the new exact solutions are shown by some figures.

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