Variational approach for breathers in a nonlinear fractional Schrodinger equation

The fractional Schrodinger 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. (C) 2018 Elsevier B.V. All rights reserved.