The conformal geometry of the Schwarzian Davey-Stewartson II hierarchy and its discrete analogue is investigated. Connections with discrete and continuous isothermic surfaces and generalised Clifford configurations are recorded. An interpretation of the Schwarzian Davey-Stewartson II flows as integrable deformations of conformally immersed surfaces is given.

The gauge equivalence between the (2+1)-dimensional Zakharov equation and (2+1)-dimensional integrable continuous Heisenberg ferromagnetic model is established. Also their integrable reductions are shown explicitly. Preprint CNLP-1994-04. Alma-Ata.1994 The concepts of gauge equivalence between completely integrable equations plays important role in the theory of solitons[1,2]. In the (2+1)-dime...

It is known that the governing equations for the evolution of the envelope of weakly nonlinear capillary-gravity wave packets, the so-called Davey-Stewartson equation, admit dromion solutions in the limit of shallow water and strong surface tension, i.e., when kh≪1 and the Bond number (Bo) ≡T/ρgh^{2}>1/3 (where T is the surface tension coefficient and h the water depth). Here we show that capil...

The (2+1)-dimensional Davey-Stewartson-like equations with variable coefficients have the applications in ultra-relativistic degenerate dense plasmas and Bose-Einstein condensates. Via Bell polynomials symbolic computation, bilinear form, Backlund transformation Lax pair for such are obtained. Based on Hirota method, we construct soliton solutions, analyze elastic collisions constant coefficien...

The dromion of the Davey-Stewartson-1 equation is studied under perturbation on the large time. In this work we construct the asymptotic solution of the Davey-Stewart-son-1 equations (DS-1): Here ε is small positive parameter, F is operator of the perturbation, the values of the parameter σ = ±1 correspond so called focusing or defocusing DS-1 equations. The equations (1) at ε = 0 describe the ...

We propose a differential difference equation in R × Z and study it by Hirota’s bilinear method. This equation has a singular continuum limit into a system which admits the reduction to the Davey-Stewartson equation. The solutions of this discrete DS system are characterized by Casorati and Grammian determinants. Based on the bilinear form of this discrete DS system, we construct the bilinear B...

This paper is concerned with the analysis of blow-up solutions to the elliptic-elliptic Davey-Stewartson system, which appears in the description of the evolution of surface water waves. We prove a mass concentration property for H-solutions, analogous to the one known for the L-critical nonlinear Schrödinger equation. We also prove a mass concentration result for L -solutions.

The classical spin model in planar condensed media is represented as the U (1) Chern-Simons gauge field theory. When the vorticity of the continuous flow of the media coincides with the statistical magnetic field, which is necessary for the model's integrability, the theory admits zero curvature connection. This allows me to formulate the model in terms of gauge-invariant fields whose evolution...

Generalized Weierstrass representations for generic surfaces confor-mally immersed into four-dimensional Euclidean and pseudo-Euclidean spaces of different signatures are presented. Integrable deformations of surfaces in these spaces generated by the Davey-Stewartson hierarchy of integrable equations are proposed. Willmore functional of a surface is invariant under such deformations.