Global Analysis for Rough Solutions to 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.

Periodic Soliton Solutions to the Davey–Stewartson Equation

The periodic soliton resonances and recurrent wave solutions to the Davey–Stewartson equation are presented. The solutions that described the interaction between a y-periodic soliton and a line soliton are analyzed to show the existence of the soliton resonances. The various recurrent solutions (The growing-and-decaying mode, breather and rational growing-anddecaying mode solutions) are present...

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...

An Implicit Finite Difference Scheme for Focusing Solutions of the Generalized Davey-stewartson System

where u and φ1, φ2 are, respectively, the complexand the real-valued functions of spatial coordinates x, y and the time t. The parameters σ, κ, γ,m1,m2, λ, n are real constants and σ is normalized as | σ |= 1. The GDS system has been derived to model 2 + 1 dimensional wave propagation in a bulk medium composed of an elastic material with couple stresses [1]. The parametric relation (λ − 1)(m2 −...

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