Spatial equation for water waves
A. I. Dyachenko+*, V. E. Zakharov+*×°
+Novosibirsk State University, 630090 Novosibirsk, Russia
*Landau Institute for Theoretical Physicsof the RAS, 142432 Chernogolovka, Russia
×Department of Mathematics, University of Arizona, AZ 857201 Tucson, USA
°Physical Institute of the RAS, 119991 Moscow, Russia
Abstract
We derive compact spatial Hamiltonian equation
for the gravity waves on the
deep water. The equation is dynamical one,
it can describe extreme waves. Also equation for envelope of wave train is
obtained.