scholarly journals Remarks on the Fundamental Solution to Schrödinger Equation with Variable Coefficients

2012 ◽  
Vol 62 (3) ◽  
pp. 1091-1121 ◽  
Author(s):  
Kenichi Ito ◽  
Shu Nakamura
Keyword(s):  
Fundamental Solution ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Variable Coefficients

Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation

2020 ◽  
Vol 21 (7-8) ◽  
pp. 675-681
Author(s):  
Rehab M. El-Shiekh ◽  
Mahmoud Gaballah
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Integration Method ◽  
Variable Coefficients ◽  
Nonlinear Schrodinger Equation ◽  
Equation Method ◽  
Direct Integration ◽  
Wave Solutions ◽  
Direct Integration Method

AbstractIn this paper, the generalized nonlinear Schrödinger equation with variable coefficients (gvcNLSE) arising in optical fiber is solved by using two different techniques the trail equation method and direct integration method. Many different new types of wave solutions like Jacobi, periodic and soliton wave solutions are obtained. From this study we have concluded that the direct integration method is more easy and straightforward than the trail equation method. As an application in optic fibers the propagation of the frequency modulated optical soliton is discussed and we have deduced that it's propagation shape is affected with the different values of both the amplification increment and the group velocity (GVD).

Bilinear forms and soliton solutions for a (2 + 1)-dimensional variable-coefficient nonlinear Schrödinger equation in an optical fiber

2020 ◽  
Vol 34 (30) ◽  
pp. 2050336
Author(s):  
Dong Wang ◽  
Yi-Tian Gao ◽  
Jing-Jing Su ◽  
Cui-Cui Ding
Keyword(s):  
Schrödinger Equation ◽  
Optical Fiber ◽  
Nonlinear Schrödinger Equation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Nonlinear Schrodinger Equation ◽  
Bilinear Forms ◽  
Dimensional Variable

In this paper, under investigation is a (2 + 1)-dimensional variable-coefficient nonlinear Schrödinger equation, which is introduced to the study of an optical fiber, where [Formula: see text] is the temporal variable, variable coefficients [Formula: see text] and [Formula: see text] are related to the group velocity dispersion, [Formula: see text] and [Formula: see text] represent the Kerr nonlinearity and linear term, respectively. Via the Hirota bilinear method, bilinear forms are obtained, and bright one-, two-, three- and N-soliton solutions as well as dark one- and two-soliton solutions are derived, where [Formula: see text] is a positive integer. Velocities and amplitudes of the bright/dark one solitons are obtained via the characteristic-line equations. With the graphical analysis, we investigate the influence of the variable coefficients on the propagation and interaction of the solitons. It is found that [Formula: see text] can only affect the phase shifts of the solitons, while [Formula: see text], [Formula: see text] and [Formula: see text] determine the amplitudes and velocities of the bright/dark solitons.

Sign in / Sign up

Export Citation Format

Share Document