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...

Many wave phenomena in physics are described by weakly nonlinear nearly monochromatic solutions in the form of modulated wave packets. The examples include ocean waves as well as waves in optics and in plasmas. There are a number of approaches to deriving the envelope equations for these theories of amplitude modulation. In this paper, we give a unified approach, based on the principles of a Ha...

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...

In this paper, based on the close relationship between the Weierstrass elliptic function ℘(ξ; g2, g3)(g2, g3, invariants) and nonlinear ordinary differential equation, a Weierstrass elliptic function expansion method is developed in terms of the Weierstrass elliptic function instead of many Jacobi elliptic functions. The mechanism is constructive and can be carried out in computer with the aid ...