Resonant solutions of the Davey–Stewartson II equation and their dynamics

Abstract

This paper aims to study the evolution dynamics of resonant solutions of the Davey–Stewartson II equation. The resonant solutions can depict diverse collision scenarios among periodic solitons themselves or among periodic solitons with algebraic decaying solitons. A significant finding in these particular collisions is the observation of wave structure transitions in the algebraic decaying solitons, along with notable changes in their dynamics. We show that the algebraic decaying solitons undergo a transition from states with non-localized behaviour in either space or time to states with localized behaviour in either space or time, or to states with localized behaviour in both time and space. The algebraic decaying solitons, exhibiting dual localization in both time and space, closely resemble two-dimensional localized waves in physical systems. They serve as effective tools for comprehending various nonlinear physical phenomena.