Geodesic
Internal solitary waves with trapped cores in multilayer shallow water
Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 2, pp. 249-263

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We consider a nonlinear system of equations that in the Boussinesq approximation describes near-bottom and near-surface large-amplitude internal waves propagating under a cover in multilayer stratified shallow water. We obtain smooth steady-state soliton-like solutions of the equations of motion in the form of symmetric and nonsymmetric mode-2 waves adjoining a given constant flow. We show that the construction of a smooth solution in which one of the layers has a finite length (trapped core) can lead to the formation of a singularity. In the class of functions with piecewise smooth first derivatives, a method for constructing solutions with trapped cores is proposed. For multilayer shallow water equations, we give examples of steady-state solutions describing soliton-like structures and flows with trapped cores.
Keywords: multilayer shallow water, internal solitary waves
Mots-clés : Boussinesq approximation. 
@article{TMF_2022_211_2_a5,
     author = {V. Yu. Lyapidevskii and A. A. Chesnokov},
     title = {Internal solitary waves with trapped cores in multilayer shallow water},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {249--263},
     publisher = {mathdoc},
     volume = {211},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_211_2_a5/}
}
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V. Yu. Lyapidevskii; A. A. Chesnokov. Internal solitary waves with trapped cores in multilayer shallow water. Teoretičeskaâ i matematičeskaâ fizika, Tome 211 (2022) no. 2, pp. 249-263. http://geodesic.mathdoc.fr/item/TMF_2022_211_2_a5/