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Travelling solitary waves in the discrete Schrödinger equation with saturable nonlinearity : Existence, stability and dynamics

 

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dc.creator Melvin, Thomas R.O.
dc.creator Champneys, A. R.
dc.creator Kevrekidis, Panayotis G.
dc.creator Cuevas-Maraver, Jesús
dc.date.accessioned 2015-05-12T07:41:02Z
dc.date.available 2015-05-12T07:41:02Z
dc.date.issued 2008
dc.identifier.issn 0167-2789 es
dc.identifier.uri http://hdl.handle.net/11441/24821
dc.description.abstract The present work examines in detail the existence, stability and dynamics of travelling solitary waves in a Schrödinger lattice with saturable nonlinearity. After analysing the linear spectrum of the problem in the travelling wave frame, a pseudo-spectral numerical method is used to identify weakly nonlocal solitary waves. By finding zeros of an appropriately crafted tail condition, we can obtain the genuinely localized pulse-like solutions. Subsequent use of continuation methods allows us to obtain the relevant branches of solutions as a function of the system parameters, such as the frequency and intersite coupling strength. We examine the stability of the solutions in two ways: both by imposing numerical perturbations and observing the solution dynamics, as well as by considering the solutions as fixed points of an appropriate map and computing the corresponding Floquet matrix and its eigenvalues. Both methods indicate that our solutions are robustly localized. Finally, the interactions of these solutions are examined in collision type phenomena, observing that relevant collisions are near-elastic, although they may, under appropriate conditions, lead to the generation of an additional pulse. es
dc.format application/pdf es
dc.language.iso eng es
dc.relation.ispartof Physica D : Nonlinear Phenomena, 237 (4),551-567 es
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional *
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ *
dc.subject Discrete nonlinear Schrödinger equation es
dc.subject Travelling waves es
dc.subject Saturable nonlinearity es
dc.subject Pseudo-spectral method es
dc.subject Stability es
dc.subject Photorefractive crystals es
dc.subject Discrete solitons es
dc.subject Numerical continuation es
dc.subject Vanishing PN barrier es
dc.title Travelling solitary waves in the discrete Schrödinger equation with saturable nonlinearity : Existence, stability and dynamics es
dc.type info:eu-repo/semantics/article es
dc.rights.accessrights info:eu-repo/semantics/openAccess es
dc.contributor.affiliation Universidad de Sevilla. Departamento de Física Aplicada I es
dc.relation.publisherversion DOI: 10.1016/j.physd.2007.09.026 es
dc.relation.publisherversion http://www.sciencedirect.com/science/article/pii/S0167278907003533 es
dc.identifier.idus https://idus.us.es/xmlui/handle/11441/24821
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