Some properties of small perturbations against a stationary solution of the nonlinear Schrodinger equation

In this paper, classical small perturbations against a stationary solution of the nonlinear Schrodinger equation with the general form of nonlinearity are examined. It is shown that in order to obtain correct (in particular, conserved over time) nonzero expressions for the basic integrals of motion of a perturbation even in the quadratic order in the expansion parameter, it is necessary to consider nonlinear equations of motion for the perturbations. It is also shown that, despite the nonlinearity of the perturbations, the additivity property is valid for the integrals of motion of different nonlinear modes forming the perturbation (at least up to the second order in the expansion parameter).Comment: 20 pages, v4: title changed; Introduction and Conclusion modified; main text slightly enlarged; references added; typos correcte

The strong coupling effect and auxiliary fields in the DGP-model

The DGP-model with additional terms in the action is considered. These terms have a special form and include auxiliary scalar fields without kinetic terms, which are non-minimally coupled to gravity. The use of these fields allows one to exclude the mode, which corresponds to the strong coupling effect, from the theory. Effective four-dimensional theory on the brane appears to be the same, as in the original DGP-model.Comment: 9 pages, LaTe

Classical behaviour of Q-balls in the Wick-Cutkosky model

In this paper, we continue discussing Q-balls in the Wick--Cutkosky model. Despite Q-balls in this model are composed of two scalar fields, they turn out to be very useful and illustrative for examining various important properties of Q-balls. In particular, in the present paper we study in detail (analytically and numerically) the problem of classical stability of Q-balls, including the nonlinear evolution of classically unstable Q-balls, as well as the behaviour of Q-balls in external fields in the non-relativistic limit.Comment: 21 pages, 12 figures, LaTeX; v2: section 3.3 slightly enlarged, typos corrected, minor changes in the tex