Comment on “Exact Self-Similar Solutions of the Generalized Nonlinear Schrödinger Equation with Distributed Coefficients”

2004 ◽  
Vol 92 (19) ◽  
Author(s):  
V. N. Serkin ◽  
Akira Hasegawa ◽  
T. L. Belyaeva
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Self Similar ◽  
Generalized Nonlinear Schrödinger Equation ◽  
Similar Solutions

Chirped Self-Similar Solutions of a Generalized Nonlinear Schrödinger Equation

2011 ◽  
Vol 66 (1-2) ◽  
pp. 1-5 ◽  
Author(s):  
Jin-Xi Fei ◽  
Chun-Long Zheng
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Balance Principle ◽  
Expansion Technique ◽  
Self Similar ◽  
Generalized Nonlinear Schrödinger Equation ◽  
Similar Solutions

An improved homogeneous balance principle and an F-expansion technique are used to construct exact chirped self-similar solutions to the generalized nonlinear Schrödinger equation with distributed dispersion, nonlinearity, and gain coefficients. Such solutions exist under certain conditions and impose constraints on the functions describing dispersion, nonlinearity, and distributed gain function. The results show that the chirp function is related only to the dispersion coefficient, however, it affects all of the system parameters, which influence the form of the wave amplitude. As few characteristic examples and some simple chirped self-similar waves are presented.

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