On the blow-up phenomenon for a generalized Davey-Stewartson system

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

Two remarks on a generalized Davey-Stewartson system

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...

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...

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...

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.