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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn026, 36 pages, doi:10.1093/imrn/rnn026 published on April 11, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Soliton Interaction with Slowly Varying Potentials

Justin Holmer and Maciej Zworski

Mathematics Department, University of California, Evans Hall, Berkeley, CA 94720, USA

Correspondence: Correspondence to be sent to: holmer{at}math.berkeley.edu

We study the Gross–Pitaevskii equation with a slowly varying smooth potential, Formula . We show that up to time Formula and errors of size Formula in Formula , the solution is a soliton, evolving according to the classical dynamics of a natural effective Hamiltonian, Formula . This provides an improvement (Formula ) compared to previous works, and is strikingly confirmed by numerical simulations.


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