scholarly journals Exact Solutions to the Nonlinear Schrödinger Equation

2010 ◽  
pp. 1-12 ◽  
Author(s):  
Tuncay Aktosun ◽  
Theresa Busse ◽  
Francesco Demontis ◽  
Cornelis van der Mee ◽  
Tuncay Aktosun ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger

scholarly journals Exact Solutions of the Generalized Nonlinear Schrodinger Equation

2021 ◽  
pp. 18-25
Author(s):  
Gaukhar Shaikhova ◽  
Arailym Syzdykova ◽  
Samgar Daulet
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Physical Problems ◽  
Different Types ◽  
Generalized Nonlinear Schrödinger Equation

In this work, the generalized nonlinear Schrodinger equation is investigated. Exact solutions are derived by the sinecosine method. This method is used to obtain the exact solutions for different types of nonlinear partial differential equations. Graphs of obtained solutions are presented. The obtained solutions are found to be important for the explanation of some practical physical problems.

scholarly journals Exact Solutions of the (2+1)-Dimensional Stochastic Chiral Nonlinear Schrödinger Equation

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1874
Author(s):  
Sahar Albosaily ◽  
Wael W. Mohammed ◽  
Mohammed A. Aiyashi ◽  
Mahmoud A. E. Abdelrahman
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Multiplicative Noise ◽  
Applied Science ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger

In this article, we take into account the (2+1)-dimensional stochastic Chiral nonlinear Schrödinger equation (2D-SCNLSE) in the Itô sense by multiplicative noise. We acquired trigonometric, rational and hyperbolic stochastic exact solutions, using three vital methods, namely Riccati–Bernoulli sub-ODE, He’s variational and sine–cosine methods. These solutions may be applicable in various applications in applied science. The proposed methods are direct, efficient and powerful. Moreover, we investigate the effect of multiplicative noise on the solution for 2D-SCNLSE by introducing some graphs to illustrate the behavior of the obtained solutions.

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