Numerical analyses of the localized structures on an uneven bottom associated with the Davey-Stewartson 1 equations

The Davey-Stewartson (DS) equations with a perturbation term are presented by taking a fluid system as an example on an uneven bottom. Stability of dromions, solutions of the DS equations with localized structures, against the perturbation is investigated numerically. Dromions decay exponentially under an effect of the perturbation, while they travel stably after the effect disappears. The decay ratio of dromions is found to have a relation to velocities of dromions. The important role played by the mean flow, which acts as an external force to the system, is discussed. These results show that dromions are quite stable as a localized structure in two dimensions, and they are expected to be observed in various physical systems such as fluid or plasma systems.