For the Davey-Stewartson I equation, which is an integrable equation in 1+2 dimensions, we have already found its Lax pair in 1+1 dimensional form by nonlinear constraints. This paper deals with the second nonlinearization of this 1+1 dimensional system to get three 1+0 dimensional Hamiltonian systems with a constraint of Neumann type. The full set of involutive conserved integrals is obtained ...

to start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ode. then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. it is required to state that the infinite series method is a well-organized method for obtaining exact s...

We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and 2 1 -dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the 2 1 dimensional Davey-Stewartson eq...

The linearized Davey-Stewartson equation with varing coefficients is solved by Fourier method. The approach uses the inverse scattering transform for the Davey-Stewartson equation.

We solve the (2+1)-dimensional Davey-Stewartson (DS) equation, a multidimensional analog of the nonlinear Schrödinger equation. A rather general solution for the variables separation with two arbitrary functions is first obtained by applying a special Bäcklund transformation and introducing the seed solutions. And then some new special types of two-dimensional coherent structures are obtained. ...

We derive the two equations of Davey-Stewartson type from a zero curvature condition associated with SL(2,R) in 2+ 1 dimensions. We show in general how a 2+1 dimensional zero curvature condition can be obtained from the self-duality condition in 3+3 dimensions and show in particular how the Davey-Stewartson equations can be obtained from the selfduality condition associated with SL(2,R) in 3 + ...

The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present paper, this essentially 1+1 dimensional Lax system is further nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann constraints. It is sho...

In this note we show that for certain choice of parameters the hyperbolic–elliptic–elliptic generalized Davey–Stewartson system admits time-dependent travelling wave solutions of the kind given in [V.A. Arkadiev, A.K. Pogrebkov, M.C. Polivanov, Inverse scattering transform method and soliton solutions for Davey–Stewartson II equation, Physica D 36 (1989) 189–197] for the hyperbolic Davey–Stewar...