Volume 136, Number 4, November 2021
|Number of page(s)||7|
|Published online||03 March 2022|
Propagation of instability fronts in modulationally unstable systems
Institute of Spectroscopy, Russian Academy of Sciences - Troitsk, Moscow, 108840, Russia and Moscow Institute of Physics and Technology - Institutsky lane 9, Dolgoprudny, Moscow region, 141701, Russia
Received: 8 December 2021
Accepted: 31 January 2022
We study the evolution of pulses propagating through focusing nonlinear media. A small disturbance of a smooth initial non-uniform pulse amplitude leads to formation of a region of strong nonlinear oscillations. We develop here an asymptotic method for finding the law of motion of the front of this region. The method is based on the conjecture that instability fronts propagate with the minimal group velocity of linear waves. To support this conjecture, at first we review several physical situations where this statement was obtained as a result of direct calculations. Then we generalize it to situations with a non-uniform flow and apply it to the focusing nonlinear Schrödinger equation for the particular cases of Talanov and Akhmanov-Sukhorukov-Khokhlov initial distributions. The approximate analytical results agree very well with the exact numerical solutions for these two problems.
© 2022 EPLA
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.