Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation
| dc.contributor.author | Sánchez, Angel | |
| dc.contributor.author | Bishop, A. R. | |
| dc.contributor.author | Domínguez-Adame Acosta, Francisco | |
| dc.date.accessioned | 2023-06-20T20:16:20Z | |
| dc.date.available | 2023-06-20T20:16:20Z | |
| dc.date.issued | 1994-05 | |
| dc.description | © 1994 The American Physical Society. We are indebted to Rainer Scharf, David Cai, and Maxi San Miguel for enlightening conversations on this research. A.S. is supported by the Ministerio de Educacion y Ciencia (Spain) and the Fulbright Fund, by Direccion General de Investigacion Cientifica y Tecnica (Spain) through Project No. PB92-0378, and by the European Union (¹tmork on Nonlinear Spatio-Temporal Structures in Semiconductor, Fluids, and Oscillator Ensembles). He also thanks the Los Alamos National Laboratory for warm hospitality and a productive atmosphere. Work at Los Alamos is performed under the auspices of the U.S. Department of Energy. | |
| dc.description.abstract | We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program that are not compatible with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a perturbative calculation that helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it reproduces accurately the observed kink dynamics. Fourth, we report on the occurrence of length-scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study. | |
| dc.description.department | Depto. de Física de Materiales | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Educación y Ciencia (MEC), España | |
| dc.description.sponsorship | Programa Fulbright | |
| dc.description.sponsorship | Dirección General de Investigación Científica y Técnica (DGICYT), España | |
| dc.description.sponsorship | Unión Europea (UE) | |
| dc.description.sponsorship | U.S. Department of Energy | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/37919 | |
| dc.identifier.doi | 10.1103/PhysRevE.49.4603 | |
| dc.identifier.issn | 1539-3755 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1103/PhysRevE.49.4603 | |
| dc.identifier.relatedurl | http://journals.aps.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/59987 | |
| dc.issue.number | 5 | |
| dc.journal.title | Physical review E | |
| dc.language.iso | eng | |
| dc.page.final | 4615 | |
| dc.page.initial | 4603 | |
| dc.publisher | American Physical Society | |
| dc.relation.projectID | PB92-0378 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 538.9 | |
| dc.subject.keyword | Nonlinear Schrodinger-equation | |
| dc.subject.keyword | Dynamics | |
| dc.subject.keyword | Potentials | |
| dc.subject.keyword | System | |
| dc.subject.keyword | Perturbations | |
| dc.subject.keyword | Solitons | |
| dc.subject.keyword | Waves | |
| dc.subject.keyword | Model | |
| dc.subject.ucm | Física de materiales | |
| dc.title | Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation | |
| dc.type | journal article | |
| dc.volume.number | 49 | |
| dcterms.references | 1. Disorder and Nonlinearity, edited by A. R. Bishop, D. K. Campbell, and St. Pnevmatikos, Springer Proceedings in Physics Vol. 39 (Springer Verlag, Berlin, 1989); Nonlinearity with Disorder, edited by F. Kh. Abdullaev, A. R. Bishop, and St. Pnevmatikos, Springer Proceedings in Physics Vol. 67 (Springer Verlag, Berlin, 1992). 2. Yu. S. Kivshar and B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989). 3. A. Sánchez and L. Vázquez, Int. J. Mod. Phys. B 5, 2825 (1991); S. A. Gredeskul and Yu. S. Kivshar, Phys. Rep. 216, 1 (1992). 4. A. Sánchez, R. Scharf, A. R. Bishop and L. Vázquez, Phys. Rev. A 45, 6031 (1992). 5. R. Scharf, Yu. S. Kivshar, A. Sánchez and A. R. Bishop, Phys. Rev. A 45, R5369 (1992). 6. R. Scharf and A. R. Bishop, Phys. Rev. E 47, 1375 (1993). 7. R. Scharf and A. R. Bishop, Phys. Rev. A 46, R2973 (1992). 8. G. S. Mkrtchyan and V. V. Shmidt, Solid State Commun. 30, 791 (1979). 9. B. A. Malomed, Phys. Lett. A 144, 351 (1990). 10. B. A. Malomed and M. I. Tribelsky, Phys. Rev. B 41, 11271 (1990). 11. A. Sánchez, F. Domí nguez Adame, and A. R. Bishop, Los Alamos National Laboratory Report No. LA UR 93 3740, 1993 (unpublished). 12. M. B. Fogel, S. E. Trullinger, A. R. Bishop and J. A. Krumhansl, Phys. Rev. Lett. 24, 1411 (1976); Phys. Rev. B 15, 1578 (1977) M. B. Fogel, S. E. Trullinger and A. R. Bishop, Phys. Lett.59A, 81 (1976). 13. A. Sánchez, L. Vázquez and V. V. Konotop, Phys. Rev. A 44, 1086 (1991). 14. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, New York, 1992). 15. M. Peyrard and M. D. Kruskal, Physica D 14, 88 (1984). 16. Z. Fei, V. V. Konotop, M. Peyrard and L. Vázquez, Phys. Rev. E 48, 548 (1993). 17. R. J. Flesch and S. E. Trullinger, J. Math. Phys. 28, 1619 (1987); A. Galindo and P. Pascual,Quantum Mechanics I (Springer Verlag, Berlin, 1990). 18. It is possible to analyze the long wavelength limit of the spectrum analytically by means of an averaging technique, which leads to the result that the minimum frequency is given by ωmin2= 1-(ε2/2k2), in good agreement with our numerical calculation of the spectrum as can be seen from the figures. 19. V. V. Konotop, A. Sánchez and L. Vázquez, Phys. Rev. B 44, 2554 (1991). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | dbc02e39-958d-4885-acfb-131220e221ba | |
| relation.isAuthorOfPublication.latestForDiscovery | dbc02e39-958d-4885-acfb-131220e221ba |
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