Simone Secchi, Marco Squassina
Soliton dynamics for fractional Schr\"odinger equations
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ABSTRACT.  We investigate the soliton dynamics for the fractional 
 nonlinear Schr\"odinger 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.