TY - JOUR

T1 - Transient radiative behavior of Hamiltonian systems in finite domains

AU - Rapti, Z.

AU - Weinstein, M. I.

AU - Kevrekidis, P. G.

PY - 2005/9/26

Y1 - 2005/9/26

N2 - We show that Hamiltonian partial differential equations on compact spatial domains can display transient radiative behavior, usually associated with infinite domains. This is done by considering a model of a single oscillator coupled to a wave field, which damps due to the resonant coupling of the oscillator with a discrete frequency with the continuous spectrum of the field. The analysis carried out illustrates that despite the "discretization" of the continuous spectrum due to the finiteness of the domain, a remnant of the resonance mechanism persists. In particular, this explains how numerical computations on bounded domains accurately simulate, on large but finite time scales, phenomena associated with infinite spatial domains. Numerical simulations in the present model show good agreement with our theoretical predictions.

AB - We show that Hamiltonian partial differential equations on compact spatial domains can display transient radiative behavior, usually associated with infinite domains. This is done by considering a model of a single oscillator coupled to a wave field, which damps due to the resonant coupling of the oscillator with a discrete frequency with the continuous spectrum of the field. The analysis carried out illustrates that despite the "discretization" of the continuous spectrum due to the finiteness of the domain, a remnant of the resonance mechanism persists. In particular, this explains how numerical computations on bounded domains accurately simulate, on large but finite time scales, phenomena associated with infinite spatial domains. Numerical simulations in the present model show good agreement with our theoretical predictions.

UR - http://www.scopus.com/inward/record.url?scp=24644462762&partnerID=8YFLogxK

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U2 - 10.1016/j.physleta.2005.07.010

DO - 10.1016/j.physleta.2005.07.010

M3 - Article

AN - SCOPUS:24644462762

SN - 0375-9601

VL - 345

SP - 1

EP - 9

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 1-3

ER -