Stewartson System Research Articles

Multi-solitons for a generalized Davey-Stewartson system

This paper studies multi-solitons of non-integrable generalized Davey-Stewartson system in the elliptic-elliptic case. By extending the method for constructing multi-solitons of non-integrable nonlinear Schrodinger equations and systems developed by Martel et al. to the present non-integrable generalized Davey- Stewartson system and overcoming some new difficulties caused by the nonlocal operator B, we prove the existence of multi-solitons for this system. Furthermore, we also give a generalization of this result to a more general class of equations with nonlocal nonlinearities.

SYMBOLIC COMPUTATION AND WEIERSTRASS ELLIPTIC FUNCTION SOLUTIONS OF THE DAVEY–STEWARTSON (DS) SYSTEM

In this paper, with the symbolic computation, the doubly-periodic solutions of the Davey–Stewartson (DS) system, which describes the modulational instability of uniform train of weakly nonlinear water waves in the two-dimensional space, are investigated in terms of the Weierstrass elliptic function ℘(ξ; g2, g3). In particular, we also give new solitary wave solutions of this system.

Global existence and asymptotic behaviour in time of small solutions to the elliptic - hyperbolic Davey - Stewartson system

We study the initial value problem for the elliptic - hyperbolic Davey - Stewartson system where , , u is a complex valued function and is a real valued function. When the above system is called a DSI equation in the inverse scattering literature. Our purpose in this paper is to prove global existence of small solutions to this system in the usual weighted Sobolev space , where Furthermore, we prove time decay estimates of solutions to the system such that

The Dirac equation and integrable systems of KP type

The propagator for the 2D heat equation in an arbitrary linear space is shown to give solutions of the two-component Kadomtsev - Petviashvilii (KP) equations, also called Davey - Stewartson system. This propagator is subject to the Klein - Gordon equation and its right-derivatives are required to be of rank one, that imply that it can be expressed in terms of solutions of the Dirac equation. Large families of solutions of the two-component Kadomtsev - Petviashvilii equations are constructed in terms of solutions of the heat and Dirac equations. Particular attention is paid to the real reductions of the Davey - Stewartson type, recovering in this way the line solitons and the multidromion solutions. Moreover, new solutions to the Davey - Stewartson I are presented as massive deformations of the dromion.