Asymptotic stability of solitary waves
dc.contributor.author | Pego, Robert L. | en_US |
dc.contributor.author | Weinstein, Michael I. | en_US |
dc.date.accessioned | 2006-09-11T17:50:36Z | |
dc.date.available | 2006-09-11T17:50:36Z | |
dc.date.issued | 1994-08 | en_US |
dc.identifier.citation | Pego, Robert L.; Weinstein, Michael I.; (1994). "Asymptotic stability of solitary waves." Communications in Mathematical Physics 164(2): 305-349. <http://hdl.handle.net/2027.42/46489> | en_US |
dc.identifier.issn | 1432-0916 | en_US |
dc.identifier.issn | 0010-3616 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/46489 | |
dc.description.abstract | We show that the family of solitary waves (1-solitons) of the Korteweg-de Vries equation is asymptotically stable. Our methods also apply for the solitary waves of a class of generalized Korteweg-de Vries equations, In particular, we study the case where f(u)=u p+1 / (p+1) , p =1, 2, 3 (and 3< p <4, for u >0, with f ∈ C 4 ). The same asymptotic stability result for KdV is also proved for the case p =2 (the modified Korteweg-de Vries equation). We also prove asymptotic stability for the family of solitary waves for all but a finite number of values of p between 3 and 4. (The solitary waves are known to undergo a transition from stability to instability as the parameter p increases beyond the critical value p =4.) The solution is decomposed into a modulating solitary wave, with time-varying speed c(t) and phase γ( t ) ( bound state part ), and an infinite dimensional perturbation ( radiating part ). The perturbation is shown to decay exponentially in time, in a local sense relative to a frame moving with the solitary wave. As p →4 − , the local decay or radiation rate decreases due to the presence of a resonance pole associated with the linearized evolution equation for solitary wave perturbations. | en_US |
dc.format.extent | 2443263 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag | en_US |
dc.subject.other | Mathematical and Computational Physics | en_US |
dc.subject.other | Relativity and Cosmology | en_US |
dc.subject.other | Physics | en_US |
dc.subject.other | Statistical Physics | en_US |
dc.subject.other | Quantum Computing, Information and Physics | en_US |
dc.subject.other | Quantum Physics | en_US |
dc.subject.other | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | en_US |
dc.title | Asymptotic stability of solitary waves | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, 48109, Ann Arbor, MI, USA | en_US |
dc.contributor.affiliationother | Department of Mathematics & Institute for Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/46489/1/220_2005_Article_BF02101705.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF02101705 | en_US |
dc.identifier.source | Communications in Mathematical Physics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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