Localized structures in surface waves

Abstract

An amplitude equation in the form of a perturbed nonlinear Schr\"odinger equation is derived for parametric excitation of surface waves in an extended system. Continuous symmetries of the unperturbed system are used to identify critical modes. Dynamical equations for the latter are derived using singular perturbation theory. The existence of a stable nonpropagating kink solution is predicted. The solution connects two uniform states whose phases of oscillations differ by \ensuremath{\pi}, and should be observable in wide enough cells. A stable nonpropagating soliton solution is found for subcritical excitation.