Numerical study of the Davey-Stewartson system

Mass Concentration for the Davey-stewartson System

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.

On a Discrete Davey-stewartson System

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...

Numerical simulation of blow-up solutions for the generalized Davey-Stewartson system

The Davey-Stewartson system and the Bäcklund Transformations

We consider the (coupled) Davey-Stewartson (DS) system and its Bäcklund transformations (BT). Relations among the Davey-Stewartson system, the double KadomtsevPetviashvili (KP) system and the Ablowitz-Ladik hierarchy (ALH) are established. The DS hierarchy and the double KP system are equivalent. The ALH is the BT of the DS system in a certain reduction. From the BT of coupled DS system we can ...

Standing waves for a generalized Davey-Stewartson system: Revisited

The existence of standing waves for a generalized Davey–Stewartson (GDS) system was shown in Eden and Erbay [8] using an unconstrainted minimization problem. Here, we consider the same problem but relax the condition on the parameters to χ+b < 0 or χ + b m1 < 0. Our approach, in the spirit of Berestycki, Gallouët and Kavian [3] and Cipolatti [6], is to use a constrained minimization problem and...