Spatial equation for water waves


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Abstract

A compact spatial Hamiltonian equation for gravity waves on deep water has been derived. The equation is dynamical and can describe extreme waves. The equation for the envelope of a wave train has also been obtained.

About the authors

A. I. Dyachenko

Novosibirsk State University; Landau Institute for Theoretical Physics

Author for correspondence.
Email: alexd@itp.ac.ru
Russian Federation, Novosibirsk, 630090; Chernogolovka, Moscow region, 142432

V. E. Zakharov

Novosibirsk State University; Landau Institute for Theoretical Physics; Department of Mathematics; Landau Physical Institute

Email: alexd@itp.ac.ru
Russian Federation, Novosibirsk, 630090; Chernogolovka, Moscow region, 142432; Tucson, AZ, 857201; Moscow, 119991

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