Geodesic
Cauchy invariants and exact solutions of nonlinear equations of
Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 2, pp. 165-175

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We review exact solutions for gravity waves in deep water. All of them are obtained within the Lagrangian framework and are generalizations of Gerstner waves (to the cases of inhomogeneous pressure on the free surface and taking the rotation of the fluid into account). The Cauchy invariants are found for each type of waves.
Keywords: Lagrangian coordinates, Gerstner wave.
Mots-clés : Cauchy invariants 
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A. A. Abrashkin; E. N. Pelinovsky. Cauchy invariants and exact solutions of nonlinear equations of. Teoretičeskaâ i matematičeskaâ fizika, Tome 215 (2023) no. 2, pp. 165-175. http://geodesic.mathdoc.fr/item/TMF_2023_215_2_a0/