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We investigate the soliton dynamics for the Schrodinger-Newton system by proving a suitable modulational stability estimates in the spirit of those obtained by Weinstein for local equations.
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We investigate the soliton dynamics for the fractional nonlinear Schrodinger equation by a suitable modulational inequality. In the semiclassical limit, the solution concentrates along a trajectory determined by a Newtonian equation depending of the fractional diffusion parameter.
The semiclassical limit of a nonlinear focusing Schrodinger equation in presence of nonconstant electric and magnetic potentials V,A is studied by taking as initial datum the ground state solution of an associated autonomous elliptic equation. The concentration curve of the solutions is a parameterization of the solutions of a Newton ODE involving the electric force as well as the magnetic force via the Lorenz law of electrodynamics.
We study the Schrodinger-Debye system over $mathbb{R}^d$ iu_t+frac 12Delta u=uv,quad mu v_t+v=lambda |u|^2 and establish the global existence and scattering of small solutions for initial data in several function spaces in dimensions $d=2,3,4$. Moreover, in dimension $d=1$, we prove a Hayashi-Naumkin modified scattering result.
The soliton dynamics in the semiclassical limit for a weakly coupled nonlinear focusing Schrodinger systems in presence of a nonconstant potential is studied by taking as initial data some rescaled ground state solutions of an associate elliptic system.
In this note, we give an alternative proof of the theorem on soliton selection for small energy solutions of nonlinear Schrodinger equations (NLS) which we studied in Anal. PDE 8 (2015), 1289-1349 and more recently in Annals of PDE (2021) 7:16. As in in the latter paper we use the notion of Refined Profile, with the difference that here we do not modify the modulation coordinates and we do not search for Darboux coordinates. This shortens considerably the proof.
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