Issue |
EPL
Volume 136, Number 4, November 2021
|
|
---|---|---|
Article Number | 40001 | |
Number of page(s) | 7 | |
Section | General | |
DOI | https://doi.org/10.1209/0295-5075/ac5083 | |
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
(a) kamch@isan.troitsk.ru (corresponding author)
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.
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