The periodic soliton resonances and recurrent wave solutions to the Davey–Stewartson equation are presented. The solutions that described the interaction between a y-periodic soliton and a line soliton are analyzed to show the existence of the soliton resonances. The various recurrent solutions (The growing-and-decaying mode, breather and rational growing-anddecaying mode solutions) are present...

We consider the ∂-Dirac system that Ablowitz and Fokas used to transform the defocussing Davey–Stewartson system to a linear evolution equation. The nonlinear Plancherel identity for the scattering transform was established by Beals–Coifman for Schwartz functions. Sung extended the validity of the identity to functions belonging to L(R) ∩ L∞(R2) and Brown to L(R)–functions with sufficiently sma...

The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step we investiga...

A family of higher-order rational lumps on non-zero constant background Davey-Stewartson (DS) II equation are investigated. These solutions have multiple peaks whose heights and trajectories approximately given by asymptotical analysis. It is found that the time-dependent for large time they approach same height value first-order fundamental lump. The resulting considered it scattering angle ca...

General rogue waves in the Davey-Stewartson-I equation are derived by the bilinear method. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background with a line profile and then disappear into the constant background again. It is also shown that multirogue waves describe the interaction of several fundamental rogue waves. These multiro...