The Davey-Stewartson 1(DS1) system[9] is an integrable model in two dimensions. A quantum DS1 system with 2 colour-components in two dimensions has been formulated. This two-dimensional problem has been reduced to two one-dimensional many-body problems with 2 colour-components. The solutions of the two-dimensional problem under consideration has been constructed from the resulting problems in o...

Many equations can be expressed as a cubic nonlinear Schrödinger (NLS) equation with additional terms, such as the Davey-Stewartson (DS) system [1]. As it is the case for the NLS equation, the solutions of the DS system are invariant under the pseudo-conformal transformation. For the elliptic NLS, this invariance plays a key role in understanding the blow-up profile of solutions, whereas in the...

The linear stability problem for the Hocking–Stewartson pulse, obtained by linearizing the complex Ginzburg–Landau (cGL) equation, is formulated in terms of the Evans function, a complex analytic function whose zeros correspond to stability exponents. A numerical algorithm based on the compound matrix method is developed for computing the Evans function. Using values in the cGL equation associa...

We used what we called extended Fan’s sub-equation method and a new compound Riccati equations rational expansion method to construct the exact travelling wave solutions of the Davey-Stewartson DS equations. The basic idea of the proposed extended Fan’s subequation method is to take fulls advantage of the general elliptic equations, involving five parameters, which have many new solutions and w...

In this paper, we study the regularity properties of solutions to Davey–Stewartson system. It is shown that for initial data in a Sobolev space, nonlinear part solution flow resides smoother space than all times. We also obtain norm evolution grows at most polynomially. As an application smoothing estimate, long-term dynamics forced and weakly damped regard, give new proof existence smoothness ...

Based on work related to the R-matrix theory, we first abstract Lax pairs proposed by Blaszak and Sergyeyev into a unified form. Then, generalized zero-curvature equation expressed Poisson bracket is exhibited. As an application of this (2+1)-dimensional integrable system obtained, from which resulting Davey–Stewartson (DS) Pavlov (gPe) are further obtained. Via use nonisospectral zero-curvatur...

The exact solutions to the Davey-Stewartson 1 equations are constructed to describe the development of a transversal solitary wave instability. Two types of plane dark soliton decays into two-dimensional solitary waves are found and analysed. It is also shown that the transversal instability of one-dimensional waveguides leads only to a shift of their drift velocity under the action of nonlocal...

The asymptotic structure of the discrete spectrum of a compressible inviscid swirling flow with arbitrary radial distributions of density, pressure and velocity is described for disturbances with large wavenumbers. It is shown that discrete eigenmodes are unstable when a criterion derived by Eckhoff & Storesletten (1978) is satisfied. In general, these modes are characterized by a length scale ...

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 ...