4 research outputs found
Classical dynamics of a two-species Bose-Einstein condensate in the presence of nonlinear maser processes
The stability analysis of a generalized Dicke model, in the semi-classical
limit, describing the interaction of a two-species Bose-Einstein condensate
driven by a quantized field in the presence of Kerr and spontaneous parametric
processes is presented. The transitions from Rabi to Josephson dynamics are
identified depending on the relative value of the involved parameters.
Symmetry-breaking dynamics are shown for both types of coherent oscillations
due to the quantized field and nonlinear optical processes.Comment: 12 pages, 5 figures. Accepted for publication as chapter in
"Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations in
Nonlinear Systems
Solitary waves for linearly coupled nonlinear Schrodinger equations with inhomogeneous coefficients
Motivated by the study of matter waves in Bose-Einstein condensates and
coupled nonlinear optical systems, we study a system of two coupled nonlinear
Schrodinger equations with inhomogeneous parameters, including a linear
coupling. For that system we prove the existence of two different kinds of
homoclinic solutions to the origin describing solitary waves of physical
relevance. We use a Krasnoselskii fixed point theorem together with a suitable
compactness criterion.Comment: 16 page
Conditions and stability analysis for saddle–node bifurcations of solitary waves in generalized nonlinear Schrödinger equations
Saddle-node bifurcations of solitary waves in generalized nonlinear Schrödinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions are analyzed. First, general conditions for these bifurcations are derived. Second, it is shown analytically that the linear stability of these solitary waves does not switch at saddle-node bifurcations, which is in stark contrast with finite-dimensional dynamical systems where stability switching takes place. Third, it is shown that this absence of stability switching does not contradict the Vakhitov–Kolokolov stability criterion or the results in finite-dimensional dynamical systems. Fourth, it is shown that this absence of stability switching holds not only for real potentials but also for complex potentials. Lastly, various numerical examples will be given to confirm these analytical findings. In particular, saddle-node bifurcations with both branches of solitary waves being stable will be presented.