Variational approach for breathers in a nonlinear fractional Schrödinger equation

•Nonlinear fractional Schrödinger equation is reformulated as a variational problem.•Predictions for evolutions of breathers give good agreement with numerical results.•Analytical oscillation period of breathers is obtained and a good fit.•Variational approach for nonlinear fractional Schrödinger eq...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2019-06, Vol.71, p.73-81
Main Authors: Chen, Manna, Guo, Qi, Lu, Daquan, Hu, Wei
Format: Article
Language:English
Subjects:
Breather
Breathers
Fractional calculus
Fractions
Lattice theory
Nonlinear Schrödinger equation
Nonlinearity
Normal distribution
Numerical prediction
Predictions
Schrodinger equation
Variational approach
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Summary:•Nonlinear fractional Schrödinger equation is reformulated as a variational problem.•Predictions for evolutions of breathers give good agreement with numerical results.•Analytical oscillation period of breathers is obtained and a good fit.•Variational approach for nonlinear fractional Schrödinger equation is valid. The fractional Schrödinger equation with a Kerr nonlinearity, is reformulated as a variational problem to predict the evolutions of breathers. Here the breather is formed from a soliton when the input power deviates little from the soliton power. By means of a Gaussian trial function, the soliton solution is analytically obtained, and the evolutionary equations for the breather are derived. When the ratio of the input power and the soliton power approaches 1, the predictions for breather evolutions give good agreement with the numerical results. In this case, the predicted analytical breather period is obtained approximately and is also a very good fit. When the soliton at higher powers, its shape is numerically found to exhibit dramatic changes during propagation, and therefore the variation approach fails to predict its evolution.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2018.11.013