This work demonstrates an innovative numerical method for counting and locating eigenvalues with the Evans function. Utilizing the geometric phase in the Hopf bundle, the technique calculates the winding of the Evans function about a contour in the spectral plane, describing the eigenvalues enclosed by the contour for the Hocking-Stewartson pulse of the complex Ginzburg-Landau equation. Locatin...

The perturbation of the dromion of the Davey-Stewartson-1 equation is studied over the large time.

The Bäcklund-Darboux transformations are successfully utilized to construct heteroclinic orbits of Davey-Stewartson II equations through an elegant iteration of the transformations. In [17], we successfully built Melnikov vectors with the gradients of Floquet discriminants. Since there is no Floquet discriminant for Davey-Stewartson equations (in contrast to nonlinear Schrödinger equations [17]...

The Davey-Stewartson equations are used to describe the long time evolution of a threedimensional packets of surface waves. Assuming that the argument functions are quadratic in spacial variables, we find in this paper various exact solutions modulo the most known symmetry transformations for the Davey-Stewartson equations.

Complex geometric optics solutions to a system of d-bar equations appearing in the context electrical impedance tomography and scattering theory integrable Davey-Stewartson II are studied for large values spectral parameter k. For potentials q ∈ ⋅ − 2 H s ℂ some 1 , it is shown that solution converges as series / k . being characteristic function strictly convex open set with smooth boundary, t...

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 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...

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. ...