Geodesic
Motion of particles in the field of nonlinear wave packets in a~liquid layer under an ice cover
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 586-600

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We consider a liquid layer of a finite depth described by Euler's equations. The ice cover is geometrically modeled by a nonlinear elastic Kirchhoff–Love plate. We determine the trajectories of liquid particles under an ice cover in the field of a nonlinear surface traveling wave rapidly decaying at infinity, namely, a solitary wave packet (a monochromatic wave under the envelope, with the wave velocity equal to the envelope velocity) of a small but finite amplitude. Our analysis is based on the use of explicit asymptotic expressions for solutions describing the wave structures at the water–ice interface of a solitary wave packet type, as well as asymptotic solutions for the velocity field generated by these waves in the depth of the liquid.
Keywords: ice cover, solitary wave packet, central manifold, trajectories of liquid particles.
Mots-clés : bifurcation 
@article{TMF_2024_218_3_a8,
     author = {A. T. Il'ichev and A. S. Savin and A. Yu. Shashkov},
     title = {Motion of particles in the field of nonlinear wave packets in a~liquid layer under an ice cover},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {586--600},
     publisher = {mathdoc},
     volume = {218},
     number = {3},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2024_218_3_a8/}
}
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A. T. Il'ichev; A. S. Savin; A. Yu. Shashkov. Motion of particles in the field of nonlinear wave packets in a~liquid layer under an ice cover. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 586-600. http://geodesic.mathdoc.fr/item/TMF_2024_218_3_a8/