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Stability of periodic waves of finite amplitude on the surface of a deep fluid
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 transformedExpand
Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media
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 inverseExpand
Collapse of Langmuir Waves
Interaction between solitons in a stable medium
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 ofExpand
Three-dimensional solitons
Analytical description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping)
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 theExpand