Abstract
A relation between the Davey - Stewartson (DS) system and the Ablowitz - Ladik hierarchy (ALH) is established. It is shown that the former can be `embedded' into the system of flows described by the ALH. This relation is used to work out a procedure for obtaining a wide range of solutions of the (2 + 1)-dimensional DS equation using the traditional inverse scattering transform that has been developed for (1 + 1)-dimensional systems, without invoking the multidimensional one. The `embedding into the ALH' method is used to derive the dark soliton, quasiperiodic and some other solutions for the DS-II as well for the Ishimori equation, which is gauge equivalent to the DS system.
Published Version
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