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Long time motion of...
Abstract
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- We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schrodinger equations with a confining, slowly varying external potential, V(x). A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential V(x) over a long time interval.
Nyckelord
- nonlinear schrodinger-equations
- scalar field-equations
- asymptotic stability
- ground-states
- nontopological solitons
- nonintegrable equations
- dissipative systems
- energy propagation
- smoothing property
- hartree equation
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