THE DAVEY-STEWARTSON EQUATION AND THE ABLOWITZ-LADIK HIERARCHY

A relation between the Davey-Stewartson (DS) system and the Ablowitz-L adik hierarchy (ALH) is established. It is shown that the former can b e 'embedded' into the system of flows described by the ALH. This relat ion is used to work out a procedure for obtaining a wide range of solu tions of the (2 + 1)-dimensional DS equation using the traditional inv erse scattering transform that has been developed for (1 + 1)-dimensio nal systems, without invoking the multidimensional one. The 'embedding into the ALH' method is used to derive the dark soliton, quasiperiodi c and some other solutions for the DS-II as well for the Ishimori equa tion, which is gauge equivalent to the DS system.