Integrable model of the~interaction of counter-propagating weakly nonlinear waves on the~fluid boundary in a~horizontal electric field
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 3, pp. 403-414
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We consider the nonlinear dynamics of the free surface of a high-permittivity dielectric fluid in a strong horizontal electric field. In the framework of the weakly nonlinear approximation where we assume that the inclination angles of the boundary are small and take only the terms quadratically nonlinear in a small parameter into account in the equations of motion, we obtain a compact model equation that describes nonlinear wave processes in the system. We use this equation to investigate the interaction of counter-propagating solitary surface waves analytically and numerically. In particular, we demonstrate that the counter-propagating waves restore their shape after the interaction and thus acquire a certain phase shift. We also show that these properties of the model originate from its integrability.
Keywords:
nonlinear wave, integrability, electric field, free fluid surface.
@article{TMF_2020_202_3_a6,
author = {N. M. Zubarev and E. A. Kochurin},
title = {Integrable model of the~interaction of counter-propagating weakly nonlinear waves on the~fluid boundary in a~horizontal electric field},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {403--414},
publisher = {mathdoc},
volume = {202},
number = {3},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2020_202_3_a6/}
}
TY - JOUR AU - N. M. Zubarev AU - E. A. Kochurin TI - Integrable model of the~interaction of counter-propagating weakly nonlinear waves on the~fluid boundary in a~horizontal electric field JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2020 SP - 403 EP - 414 VL - 202 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2020_202_3_a6/ LA - ru ID - TMF_2020_202_3_a6 ER -
%0 Journal Article %A N. M. Zubarev %A E. A. Kochurin %T Integrable model of the~interaction of counter-propagating weakly nonlinear waves on the~fluid boundary in a~horizontal electric field %J Teoretičeskaâ i matematičeskaâ fizika %D 2020 %P 403-414 %V 202 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2020_202_3_a6/ %G ru %F TMF_2020_202_3_a6
N. M. Zubarev; E. A. Kochurin. Integrable model of the~interaction of counter-propagating weakly nonlinear waves on the~fluid boundary in a~horizontal electric field. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 3, pp. 403-414. http://geodesic.mathdoc.fr/item/TMF_2020_202_3_a6/