A plethora of generalised solitary gravity–capillary water waves

A plethora of generalised solitary gravity-capillary water waves

Shallow Water Waves and Solitary Waves

Glossary Deep water A surface wave is said to be in deep water if its wavelength is much shorter than the local water depth. Internal wave A internal wave travels within the interior of a fluid. The maximum velocity and maximum amplitude occur within the fluid or at an internal boundary (interface). Internal waves depend on the density-stratification of the fluid. Shallow water A surface wave i...

Transverse instabilities of deep-water solitary waves

The dynamics of a one-dimensional slowly modulated, nearly monochromatic localized wave train in deep water is described by a one-dimensional soliton solution of a twodimensional nonlinear Schrödinger (NLS) equation. In this paper, the instability of such a wave train with respect to transverse perturbations is examined numerically in the context of the NLS equation, using Hill’s method. A vari...

Instability of large solitary water waves

We consider the linearized instability of 2D irrotational solitary water waves. The maxima of energy and the travel speed of solitary waves are not obtained at the highest wave, which has the 120 degree angle at the crest. Under the assumption of non-existence of secondary bifurcation which is con…rmed numerically, we prove linear instability of solitary waves which are higher than the wave of ...

Symmetry of Solitary Water Waves with Vorticity

Symmetry and monotonicity properties of solitary water-waves of positive elevation with supercritical values of parameter are established for an arbitrary vorticity. The proof uses the detailed knowledge of asymptotic decay of supercritical solitary waves at infinity and the method of moving planes.