Soliton Dynamics for Fractional Schrödinger Equations
نویسنده
چکیده
We investigate the soliton dynamics for the fractional nonlinear Schrödinger 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.
منابع مشابه
Collision Dynamics of Polarized Solitons in Linearly Coupled Nonlinear Schrödinger Equations
The system of linearly coupled nonlinear Schrödinger equations is solved by a conservative difference scheme in complex arithmetic. The initial condition represents a superposition of two one-soliton solutions of linear polarizations. The head-on and takeover interaction of the solitons and their quasi-particle (QP) behavior is examined in conditions of rotational polarization and gain. We foun...
متن کاملSoliton Solutions for Quasilinear Schrödinger Equations, I
For a class of quasilinear Schrödinger equations we establish the existence of ground states of soliton type solutions by a minimization argument.
متن کاملPerturbation Expansion and N -th Order Fermi Golden Rule of the Nonlinear Schrödinger Equations
In this paper we consider generalized nonlinear Schrödinger equations with external potentials. we compute the forth and the sixed order Fermi Golden Rules (FGR), conjectured in [GS2, GS3], which is used in a study of the asymptotic dynamics of trapped solitons.
متن کاملDynamics of Nonlinear Schrödinger /Gross-Pitaevskii Equations; Mass Transfer in Systems with Solitons and Degenerate Neutral Modes
Nonlinear Schrödinger / Gross-Pitaevskii equations play a central role in the understanding of nonlinear optical and macroscopic quantum systems. The large time dynamics of such systems is governed by interactions of the nonlinear ground state manifold, discrete neutral modes (“excited states”) and dispersive radiation. Systems with symmetry, in spatial dimensions larger than one, typically hav...
متن کامل