scholarly journals Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Imre F. Barna ◽  
Mihály A. Pocsai ◽  
L. Mátyás
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Term ◽  
Nonlinear Schrodinger Equation ◽  
Similarity Analysis ◽  
System Of Differential Equations ◽  
Self Similarity ◽  
Nonlinear Schrödinger ◽  
Highly Nonlinear

In the present study a particular case of Gross-Pitaevskii or nonlinear Schrödinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation. The obtained system of differential equations is highly nonlinear. Regarding the solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case.

Optical wave solutions of the higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term via modified Khater method

2020 ◽  
Vol 34 (05) ◽  
pp. 2050044 ◽  
Author(s):  
Raghda A. M. Attia ◽  
Dianchen Lu ◽  
Turgut Ak ◽  
Mostafa M. A. Khater
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Pulse Propagation ◽  
Nonlinear Term ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Highly Nonlinear

This research paper studies the optical soliton wave solutions of the model of sub-10-fs-pulse propagation by the implementation of the modified Khater method. This model describes the dynamics of light pulses that represent a higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term. The validity of this model depends on one primary hypothesis, which is the carrier wavelength of the soliton is much shorter than the spatial width. This means that the amplitude of the soliton frequency must be less than the carrier frequency. The shorter femtosecond pulses ([Formula: see text]100 fs) are desired to increase the bit rate of pulse propagation. The losing of distribution in such short-wavelength pulses through waveguides is a negligible loss. Our solitary analytical wave solutions are approved with the waveguide made of highly nonlinear optical materials.

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