Solitary wave interactions with continuous waves

Solitary wave propagation under interaction with continuous waves is studied in the context of the Nonlinear Schrodinger Equation. An analytical approach, based on the conserved quantities of the wave evolution, is used to study transverse velocity variations for the case of nonzero transverse wavenumber difference between the solitary and continuous waves. The method is applicable for any number of transverse dimensions and any kind of nonlinearity. Moreover, the presence of a coherent continuous background is shown to be responsible for the creation of solitary rings and spirals, under interaction with solitary structures with nonzero topological charge. Numerical simulations for specific cases were used to confirm the analytical results.