Bound states of topological defects in parametrically excited capillary waves

Bound states of topological defects arising in a tetragonal lattice formed by two orthogonal standing parametrically excited capillary surface waves are investigated. Such bound states are shown to consist either of two topological charges of one sign (type 1) or of topological charges having opposite signs (type 2). It was found that bound states of type 1 move primarily along wave fronts, and type 2 bound states move at an angle of 45 deg to the wave fronts forming a tetragonal lattice. A system of four coupled Ginzburg-Landau equations is proposed to model bound states. Numerical modeling of this system gave solutions corresponding to type 1 bound states observed in experiment.