Solitary wave dynamics in an external potential
We study the behavior of solitary-wave solutions of some generalized nonlinear Schrodinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing inertial motions of stable solitary waves. We consider solutio...
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Published in | Communications in mathematical physics Vol. 250; no. 3; pp. 613 - 642 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Heidelberg
Springer
01.10.2004
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Subjects | |
Online Access | Get full text |
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Summary: | We study the behavior of solitary-wave solutions of some generalized nonlinear Schrodinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing inertial motions of stable solitary waves. We consider solutions of the equations with a non-vanishing external potential corresponding to initial conditions close to one of these solitary wave solutions and show that, over a large interval of time, they describe a solitary wave whose center of mass motion is a solution of Newton's equations of motion for a point particle in the given external potential, up to small corrections corresponding to radiation damping. |
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ISSN: | 0010-3616 1432-0916 1432-0916 |
DOI: | 10.1007/s00220-004-1128-1 |