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Dynamics of nonlinear
Schrödinger/Gross–Pitaevskii equations: mass transfer in
systems with solitons and degenerate neutral modes
Zhou Gang and Michael I. Weinstein |
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Vol. 1 (2008), No. 3, 267–322
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Abstract |
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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 have degenerate neutral modes. Thus, we study the large time dynamics of systems with degenerate neutral modes. This requires a new normal form (nonlinear matrix Fermi Golden Rule) governing the system’s large time asymptotic relaxation to the ground state (soliton) manifold. |
Keywords
soliton, nonlinear bound state, nonlinear scattering,
asymptotic stability, dispersive partial differential
equation
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Mathematical Subject Classification 2000
Primary: 35Q51, 37K40, 37K45
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Milestones
Received: 9 January 2008
Revised: 14 July 2008
Accepted: 22 October 2008
Published: 18 December 2008
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Authors |
| Zhou Gang | |
| Department of Mathematics Princeton University Princeton, NJ United States |
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| Michael I. Weinstein | |
| Department of Applied Physics and
Applied Mathematics Columbia University New York, NY 10027 United States |
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| http://www.columbia.edu/~miw2103/ | |
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