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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Bibliographic Details
Published inAnnales Henri Poincaré Vol. 7; no. 4; pp. 621 - 660
Main Authors JONSSON, B. Lars G, FRÖHLICH, Jurg, GUSTAFSON, Stephen, SIGAL, Israel Michael
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 01.06.2006
Subjects
asymptotic stability
dissipative systems
energy propagation
Exact sciences and technology
ground-states
hartree equation
Mathematical analysis
Mathematics
nonintegrable equations
nonlinear schrodinger-equations
nontopological solitons
Partial differential equations
scalar field-equations
Sciences and techniques of general use
smoothing property
Non linear equation
Solitary wave
Center of mass
Generalized equation
Potential
Long time motion
Motion control
Schrödinger equation
Mathematical physics
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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.
ISSN:1424-0637
1424-0661
1424-0661
DOI:10.1007/s00023-006-0263-y