Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA note on small data soliton selection for nonlinear Schrodinger equations with potential
113
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
In this short note, we present a construction for the log-log blow up solutions to focusing mass-critical stochastic nonlinear Schroidnger equations with multiplicative noises. The solution is understood in the sense of controlled rough path as in cite{SZ20}.
In this note, we consider discrete nonlinear Klein-Gordon equations with potential. By the pioneering work of Sigal, it is known that for the continuous nonlinear Klein-Gordon equation, no small time periodic solution exists generically. However, for the discrete nonlinear Klein-Gordon equations, we show that there exist small time periodic solutions.
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.
We study the Cauchy problem for the generalized elliptic and non-elliptic derivative nonlinear Schrodinger equations, the existence of the scattering operators and the global well posedness of solutions with small data in Besov spaces and in modulation spaces are obtained. In one spatial dimension, we get the sharp well posedness result with small data in critical homogeneous Besov spaces. As a by-product, the existence of the scattering operators with small data is also shown. In order to show these results, the glob
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
