Long time motion of NLS solitary waves in a confining potential
We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schrodinger equations with a confining, slowly varying external potential, V(x). A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitar...
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Published in | Annales Henri Poincaré Vol. 7; no. 4; pp. 621 - 660 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Heidelberg
Springer
01.06.2006
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Subjects | |
Online Access | Get full text |
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Summary: | We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schrodinger equations with a confining, slowly varying external potential, V(x). A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential V(x) over a long time interval. |
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ISSN: | 1424-0637 1424-0661 1424-0661 |
DOI: | 10.1007/s00023-006-0263-y |