We consider the standing waves for the Davey-Stewartson systemin R* and R~. By reducing this system to a single nonlinear equation of Schradinger type, we study the existence, the regularity and asyrnptotics of ground states.
By means of new general variational method we report a direct solution for the quintic self-focusing nonlinearity and cubic-quintic 1D Gross Pitaeskii equation (GPE) in a harmonic confined potential. We explore the influence of the 3D transversal motion generating a quintic nonlinear term on the ideal 1D pure cigar-like shape model for the attractive and repulsive atom-atom interaction in Bose Einstein condensates (BEC). Also, we offer a closed analytical expression for the evaluation of the error produced when solely the cubic nonlinear GPE is considered for the description of 1D BEC.
In this paper we consider the inverse problem of recovering the viscosity coefficient in a dissipative wave equation via boundary measurements. We obtain stability estimates by considering all possible measurements implemented on the boundary. We also prove that the viscosity coefficient is uniquely determined by a finite number of measurements on the boundary provided that it belongs to a given finite dimensional vector space. 2005 Elsevier Inc. All rights reserved.
We show that the GPE with cubic nonlinearity, as a model to describe the one dimensional Bose-Einstein condensates loaded into a harmonically confined optical lattice, presents a set of ground states which is orbitally stable for any value of the self-interaction (attractive and repulsive) parameter and laser intensity. We also derive a new formalism which gives explicit expressions for the minimum energy E min and the associated chemical potential µ 0 . Based on these formulas, we generalize the variational method to obtain approximate solutions, at any order of approximation, for E min , µ 0 and the ground state.
We prove that the pseudo-conformal group of the Schrödinger equation acts on solutions of the Davey-Stewartson system and that there exists an infinite family of solutions which are invariant under the action of that group. We also exhibit two different time behaviors for these invariant solutions of the Davey-Stewartson system, and we study the stability of some of these solutions, and prove that initial data close to them give rise to global solutions asymptotically behaving like an invariant solution.
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