Solitary Wave Dynamics in an External Potential
Frohlich, J. ; Gustafson, S. ; Jonsson, B. L. G. ; Sigal, I. M.
arXiv, 0309053 / Harvested from arXiv
Text on arXiv
We study the behavior of solitary-wave solutions of some generalized nonlinear Schr\"odinger 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 construct 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.
Publié le : 2003-09-23
Classification:  Mathematical Physics,  Mathematics - Analysis of PDEs,  35Q55,  37K40,  37K05,  70K40 
@article{0309053,
     author = {Frohlich, J. and Gustafson, S. and Jonsson, B. L. G. and Sigal, I. M.},
     title = {Solitary Wave Dynamics in an External Potential},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0309053}
}

Frohlich, J.; Gustafson, S.; Jonsson, B. L. G.; Sigal, I. M. Solitary Wave Dynamics in an External Potential. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0309053/