We study the stability of steady nonlinear waves on the surface of an infinitely deep fluid [1, 2]. In section 1, the equations of hydrodynamics for an ideal fluid with a free surface are transformed… Expand

It is demonstrated that the equation iol/J/ot + l/Jxx + K 1¢12 1/1 = 0, which describes plane self-focusing and one-dimensional self-modulation can be solved exactly by reducing it to the inverse… Expand

is encountered in various physical problems. Gross [1J and Pitaevskil' [2J, and later on Tsuzuki [3J, used this equation to describe the oscillations of a Bose gas at zero temperature. The problem of… Expand

Abstract Using the combination of the canonical formalism for free-surface hydrodynamics and conformal mapping to the half-plane we obtain a simple system of pseudo-differential equations for the… Expand