It is shown that there exists a solution of Nekrasov's integral equation which corresponds to
the existence of a wave of greatest height and of permanent form moving on the surface of …

This paper investigates the flow near the summit of steep, progressive gravity wave when
the crest is still rounded but the flow is approaching Stokes's corner flow. The natural length …

This paper concerns steady plane periodic waves on the surface of an ideal liquid flowing
above a horizontal bottom. The flow is irrotational. The volume flow rate is denoted by Q, the …

Some new relations are given between the kinetic and potential energies of a solitary wave.
In particular, the Lagrangian is expressed as an integral involving the total energy …

It is shown that all supercritical solitary wave solutions to the equations for water waves are
symmetric, and monotone on either side of the crest. The proof is based on the Alexandrov …

A detailed discussion of Nekrasov's approach to the steady water-wave problems leads to a
new integral equation formulation of the periodic problem. This development allows the …

Considered here are detailed aspects of solitary-wave solutions of nonlinear evolution
equations including the Euler equations for the propagation of gravity waves on the surface …

This paper considers two-dimensional gravity solitary waves moving through a body of
density stratified water lying below vacuum. The fluid domain is assumed to lie above an …

Previous estimates of the speed of solitary waves in shallow water unexpectedly showed
that the speed and energy were greatest for waves of less than the maximum possible …

We prove the existence of solitary traveling wave solutions for an equation describing the
evolution of the free surface for waves of moderate amplitude in the shallow water regime …