Different forms for nonlinear standing waves in deep water

On Nonlinear Water Waves in a Channel

Nash-Moser Theory for Standing Water Waves

Nonlinear standing waves in Couette-Taylor flow.

A nonlinear stability analysis by Demay and looss [J. Mec. Theor. Appl. , special issue, p. 193 (1984)] of flow between concentric rotating cylinders (the Couette-Taylor system) predicted a transition from the basic flow to a state with ribbons, which are traveling waves in the azimuthal direction but standing waves in the axial direction. We have observed the transition to ribbons in laborator...

Standing waves in nonlinear Schrödinger equations

In the theory of nonlinear Schrödinger equations, it is expected that the solutions will either spread out because of the dispersive effect of the linear part of the equation or concentrate at one or several points because of nonlinear effects. In some remarkable cases, these behaviors counterbalance and special solutions that neither disperse nor focus appear, the so-called standing waves. For...

New standing solitary waves in water.

By means of the parametric excitation of water waves in a Hele-Shaw cell, we report the existence of two new types of highly localized, standing surface waves of large amplitude. They are, respectively, of odd and even symmetry. Both standing waves oscillate subharmonically with the forcing frequency. The two-dimensional even pattern presents a certain similarity in the shape with the 3D axisym...