Introduction: Inverse scattering transform holds a central place in the analysis of nonlinear integrable system in either (1+1)or (2+1)-dimensions [1]. On the other hand it has been found that explicit soliton solutions can also be obtained by the use of Bäcklund transformations in a much easier way [2]. These Bäcklund transformations are also useful in proving the superposition formulae for th...

A new (scalar) spectral decomposition is found for the Dirac system in two dimensions associated to the focusing Davey–Stewartson II (DSII) equation. Discrete spectrum in the spectral problem corresponds to eigenvalues embedded into a two-dimensional essential spectrum. We show that these embedded eigenvalues are structurally unstable under small variations of the initial data. This instability...

We show that the classical non-abelian pure Chern-Simons action is related in a natural way to completely integrable systems of the Davey-Stewartson hyerarchy, via reductions of the gauge connection in Hermitian spaces and by performing certain gauge choices. The Bäcklund Transformations are interpreted in terms of Chern-Simons equations of motion or, on the other hand, as a consistency conditi...

We introduce two powerful methods to solve the Davey-Stewartson equations: one is the homotopy perturbation method (HPM) and the other is the homotopy analysis method (HAM). HAM is a strong and easy to use analytic tool for nonlinear problems. Comparison of the HPM results with the HAM results, and compute the absolute errors between the exact solutions of the DS equations with the HPM solution...

The Davey Stewartson hierarchy will be developed based on a set of three matrix differential operators. These equations will act as evolution equations for different types of surface deformation in Euclidean four space. The Weierstrass representation for surfaces will be developed and its uniqueness up to gauge transformations will be reviewed. Applications of the hierarchy will be given with r...

Abstract A phenomenon of ice rings in Lake Baikal is considered. hydrodynamic theory proposed according to which geostrophic vortices form under the area near rings. These are due bed relief, namely, underwater canyons; therefore, they referred as canyon vortices. It shown that a divergent ring vortex forms domain at crossing vertical cylindrical Stewartson layer on lateral surface and under-ic...