Radial solutions with bounded H^1 norm decompose asymptotically into a free wave and a weakly localized component, for a broad class of nonlinear and time-dependent interactions.
Asymptotic stability of N-soliton states of NLS
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The focusing nonlinear Schrodinger equation possesses special non-dispersive solitary type solutions, solitons. Under certain spectral assumptions we show existence and asymptotic stability of solutions with the asymptoic profile (as time goes to infinity) of a linear combination of N non-colliding solitons.
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The large time asymptotics of nonlinear multichannel Schroedinger equations
Radial solutions with bounded H^1 norm decompose asymptotically into a free wave and a weakly localized component, for a broad class of nonlinear and time-dependent interactions.