dc.creator | Quintero, Niurka R. | |
dc.creator | Mertens, Franz G. | |
dc.creator | Bishop, Alan R. | |
dc.date.accessioned | 2015-08-24T10:46:50Z | |
dc.date.available | 2015-08-24T10:46:50Z | |
dc.date.issued | 2015 | |
dc.identifier.issn | 1539-3755 | es |
dc.identifier.issn | 1550-2376 | es |
dc.identifier.uri | http://hdl.handle.net/11441/28044 | |
dc.description.abstract | A stability criterion for solitons of the driven nonlinear Schrödinger equation (NLSE) has been conjectured. The criterion states that p′(v)<0 is a sufficient condition for instability, while p′(v)>0 is a necessary condition for stability; here, v is the soliton velocity and p=P/N, where P and N are the soliton momentum and norm, respectively. To date, the curve p(v) was calculated approximately by a collective coordinate theory, and the criterion was confirmed by simulations. The goal of this paper is to calculate p(v) exactly for several classes and cases of the generalized NLSE: a soliton moving in a real potential, in particular a time-dependent ramp potential, and a time-dependent confining quadratic potential, where the nonlinearity in the NLSE also has a time-dependent coefficient. Moreover, we investigate a logarithmic and a cubic NLSE with a time-independent quadratic potential well. In the latter case, there is a bisoliton solution that consists of two solitons with asymmetric shapes, forming a bound state in which the shapes and the separation distance oscillate. Finally, we consider a cubic NLSE with parametric driving. In all cases, the p(v) curve is calculated either analytically or numerically, and the stability criterion is confirmed. | es |
dc.description.sponsorship | Grant No. 1146358 STP from the Alexander von Humboldt-Stiftung, Germany, through Research Fellowship for Experienced Researchers SPA | es |
dc.description.sponsorship | MICINN (Spain) through FIS2011-24540 | es |
dc.description.sponsorship | Projects No. FQM207, No. P11-FQM7276, and No. P09-FQM-4643 by Junta de Andalucia (Spain) | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | American Physical Society | es |
dc.relation.ispartof | Physical Review E, 91(1), 012905: 1-9 | es |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.title | Soliton stability criterion for generalized nonlinear Schrödinger equations | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Física Aplicada I | es |
dc.relation.publisherversion | http://journals.aps.org/pre/abstract/10.1103/PhysRevE.91.012905 | es |
dc.relation.publisherversion | http://dx.doi.org/10.1103/PhysRevE.91.012905 | |
dc.identifier.doi | 10.1103/PhysRevE.91.012905 | |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/28044 | |