Fully- and weakly-nonlinear biperiodic traveling waves in shallow water

Nonlinear edge waves and shallow-water theory

Nonlinear refraction-diffraction of waves in shallow water

The parabolic approximation is developed to study the combined refraction/diffraction of weakly nonlinear shallow-water waves. Two methods of approach are used. In the first method Boussinesq equations are used to derive evolution equations for spectral-wave components in a slowly varying two-dimensional domain. The second method modifies the K-P equation (Kadomtsev & Petviashvili 1970) to incl...

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations.

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical m...

On Nonlinear Water Waves in a Channel

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...