Discrete Nonlinear Schrodinger Equations Free of the Peierls-Nabarro Potential

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dc.creatorDmitriev, S. V.
dc.creatorKevrekidis, P. G.
dc.creatorSukhorukov, A. A.
dc.creatorYoshikawa, N.
dc.creatorTakeno, S.
dc.date2006-03-23
dc.date2006-08-07
dc.date.accessioned2026-07-07T07:07:28Z
dc.date.available2026-07-07T07:07:28Z
dc.descriptionWe derive a class of discrete nonlinear Schr{ö}dinger (DNLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic problem. It is demonstrated that the derived class of discretizations contains subclasses conserving classical norm or a modified norm and classical momentum. These equations are interesting from the physical standpoint since they support stationary discrete solitons free of the Peierls-Nabarro potential. As a consequence, even in highly-discrete regimes, solitons are not trapped by the lattice and they can be accelerated by even weak external fields. Focusing on the cubic nonlinearity we then consider a small perturbation around stationary soliton solutions and, solving corresponding eigenvalue problem, we (i) demonstrate that solitons are stable; (ii) show that they have two additional zero-frequency modes responsible for their effective translational invariance; (iii) derive semi-analytical solutions for discrete solitons moving at slow speed. To highlight the unusual properties of solitons in the new discrete models we compare them with that of the classical DNLS equation giving several numerical examples.
dc.descriptionMisprints noticed in the journal publication are corrected [in Eq. (1) and Eq. (34)]
dc.identifierhttps://arxiv.org/abs/nlin/0603047
dc.identifierhttp://arxiv.org/abs/nlin/0603047
dc.identifierPhys. Lett. A 356, 324-332 (2006)
dc.identifierdoi:10.1016/j.physleta.2006.03.056
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110404
dc.subjectPattern Formation and Solitons
dc.subjectExactly Solvable and Integrable Systems
dc.titleDiscrete Nonlinear Schrodinger Equations Free of the Peierls-Nabarro Potential
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