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5 - Adiabatic Effective Dynamics of Solitons

Published online by Cambridge University Press:  17 September 2021

Alexander Komech  and
Elena Kopylova
Alexander Komech
Affiliation:
Universität Wien, Austria
Elena Kopylova
Affiliation:
Universität Wien, Austria
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Summary

In this chapter we explain the resultson effective dynamics of solitons in slowly varying external potentials. We also present a list of further generalizations due to J. Fröhlich, S. Gustafson, B. L. G. Jonsson, I. M. Sigal, D. Stuart, T.-P. Tsai, H.-T. Yau, and others. Moreover, we comment on the relation to the mass--energy equivalence of Einstein.

Keywords

solitonsolitary manifoldeffective dynamicsadiabatic asymptoticseffective Hamiltonian Hamiltonian structureHamiltonian canonical formslowly varying potentialeffective dispersion relationmass--energy equivalence
Type
Chapter
Information
Attractors of Hamiltonian Nonlinear Partial Differential Equations , pp. 166 - 169
Publisher: Cambridge University Press
Print publication year: 2021

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