The problem of existence of solitary wave solutions to some higher-order model evolution
equations arising from water wave theory is discussed. A simple direct method for finding …

This book is a self-contained introduction to the theory of periodic, progressive, permanent
waves on the surface of incompressible inviscid fluid. The problem of permanent water …

We prove the existence of solitary water waves of elevation, as exact solutions of the
equations of steady inviscid flow, taking into account the effect of surface tension on the free …

Capillary-gravity solitary waves with damped oscillations are studied analytically. The
analysis follows the work of Iooss and Kirchgässner who proved that these waves exist for …

A model equation derived by K adomtsev & P etviashvili (Sov Phys Dokl 15: 539–541, 1970)
suggests that the hydrodynamic problem for three-dimensional water waves with strong …

The latest results relating to the theory of nonlinear waves in dispersive and dissipative
media are reviewed. Attention is concentrated on small-amplitude solitary waves and, in …

The mathematical study of travelling waves, in the context of two-dimensional potential flows
in one or several layers of perfect fluid (s) and in the presence of free surface and interfaces …

The solitary water wave problem is to find steady free surface waves which approach a
constant level of depth in the far field. The main result is the existence of a family of exact …

This paper presents existence theories for several families of small-amplitude solitary-wave
solutions to the classical two-dimensional water-wave problem in the presence of surface …

A recently discovered phenomenon of capillary-gravity waves on water is a solitary wave of
elevation plus small-amplitude ripples at infinity. It has been conjectured by Beale [Comm …