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Propagation of solitons in a two-dimensional nonlinear square lattice

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dc.affiliation.dptoUC3M. Departamento de Mecánica de Medios Continuos y Teoría de Estructurases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Dinámica y Fractura de Elementos Estructuraleses
dc.contributor.authorZaera, Ramón
dc.contributor.authorVila Morán, Javier
dc.contributor.authorFernández-Sáez, José
dc.contributor.authorRuzzene, Massimo
dc.contributor.funderMinisterio de Ciencia e Innovación (España)es
dc.date.accessioned2023-01-10T11:41:34Z
dc.date.available2023-01-10T11:41:34Z
dc.date.issued2018-11-01
dc.description.abstractWe investigate the existence of solitary waves in a nonlinear square spring-mass lattice. In the lattice, the masses interact with their neighbors through linear springs, and are connected to the ground by a nonlinear spring whose force is expressed as a polynomial function of the masses out-of-plane displacement. The low-order Taylor series expansions of the discrete equations lead to a continuum representation that holds in the long wavelength limit. Under this assumption, solitary wave solutions are sought within the long wavelength approximation, and the subsequent application of multiple scales to the resulting nonlinear continuum equations. The study focuses on weak nonlinearities of the ground stiffness and reveals the existence of 3 types of solitons, namely a bright, a dark, and a vortex soliton. These solitons result from the balance of dispersive and nonlinear effects in the lattice, setting aside other relevant phenomena in 2D waves such as diffraction that may lead to a field that does not change during propagation in nonlinear media. For equal constants of the in-plane springs, the governing equation reduces to the Klein-Gordon type, for which bright and dark solitons replicate solutions for one-dimensional lattices. However, unequal constants of the in-plane springs aligned with the two principal lattice directions lead to conditions in which the soliton propagation direction, defined by the group velocity, differs from the wave vector direction, which is unique to two-dimensional assemblies. Furthermore, vortex solitons are obtained for isotropic lattices, which shows similarities with results previously found in optics, thermal media and quantum plasmas. The paper describes the main parameters defining the existence of these solitary waves, and verifies the analytical predictions through numerical simulations. Results show the validity of obtained solutions and illustrate the main characteristics of the solitary waves found in the considered nen
dc.description.sponsorshipM. Ruzzene acknowledges the support of the UC3M-Santander Chairs of Excellence Program during academic year 2016-17. J. Vila Moran acknowledges the support from the US National Science Foundation (Grant number 1332862). The authors from the Universidad Carlos III de Madrid are indebted to the Ministerio de Ciencia e Innovación de España (Project DPI-2014-57989-P) for the financial support.en
dc.format.extent17es
dc.identifier.bibliographicCitationZaera, R., Vila, J., Fernandez-Saez, J., & Ruzzene, M. (2018). Propagation of solitons in a two-dimensional nonlinear square lattice. International Journal of Non-Linear Mechanics, 106, 188–204.en
dc.identifier.doihttps://doi.org/10.1016/j.ijnonlinmec.2018.08.002
dc.identifier.issn0020-7462
dc.identifier.issn1878-5638 (online)
dc.identifier.publicationfirstpage188es
dc.identifier.publicationlastpage204es
dc.identifier.publicationtitleInternational Journal of Non-Linear Mechanicsen
dc.identifier.publicationvolume106es
dc.identifier.urihttps://hdl.handle.net/10016/36233
dc.identifier.uxxiAR/0000022760
dc.language.isoengen
dc.publisherElsevieren
dc.relation.projectIDGobierno de España. DPI2014-57989-Pes
dc.rights© 2018 The Authors. Published by Elsevier Ltd.en
dc.rightsThis is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).en
dc.rightsAtribución 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/es/*
dc.subject.ecienciaIngeniería Mecánicaes
dc.subject.ecienciaMaterialeses
dc.subject.otherNonlinear wave propagationen
dc.subject.other2d anisotropic latticeen
dc.subject.otherMultiple-scale expansionen
dc.subject.otherBright solitonen
dc.subject.otherDark solitonen
dc.subject.otherVortex solitonen
dc.subject.otherOptical vortex solitonsen
dc.subject.otherSchrodinger-equationen
dc.subject.otherWavesen
dc.subject.otherStabilityen
dc.subject.otherBulletsen
dc.subject.otherMediaen
dc.titlePropagation of solitons in a two-dimensional nonlinear square latticeen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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