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Nonlocal and nonlinear dispersion in a nonlinear Schrödinger-type equation: exotic solitons and short-wavelength instabilitiesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2004 (English)In: Physica D: Nonlinear Phenomena, ISSN 0167-2789, Vol. 198, no 1-2, p. 29-50Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2004. Vol. 198, no 1-2, p. 29-50
##### Keyword [en]

Nonlinear Schrödinger, Nonlinear dispersion, Nonlocal dispersion, Exotic solitons, Modulational instability
##### National Category

Natural Sciences
##### Identifiers

URN: urn:nbn:se:liu:diva-14238DOI: 10.1016/j.physd.2004.08.007OAI: oai:DiVA.org:liu-14238DiVA, id: diva2:22967
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Available from: 2007-01-26 Created: 2007-01-26 Last updated: 2014-01-13
##### In thesis

We study the continuum limit of a nonlinear Schrödinger lattice model with both on-site and inter-site nonlinearities, describing weakly coupled optical waveguides or Bose–Einstein condensates. The resulting continuum nonlinear Schrödinger-type equation includes both nonlocal and nonlinear dispersion. Looking for stationary solutions, the equation is reduced to an ordinary differential equation with a rescaled spectral parameter and a single parameter interpolating between the nonlocality and the nonlinear dispersion. It is seen that these two effects give a similar behaviour for the solutions. We find smooth solitons and, beyond a critical value of the spectral parameter, also nonanalytic solitons in the form of peakons and *capons*. The existence of the exotic solitons is connected to the special properties of the phase space of the equation. Stability is investigated numerically by calculating eigenvalues and eigenfunctions of the linearized problem, and we particularly find that with both nonlocal and nonlinear dispersion simultaneously present, all solutions are unstable with respect to a break-up into short-wavelength oscillations.

1. Stability and Mobility of Localized and Extended Excitations in Nonlinear Schrödinger Models$(function(){PrimeFaces.cw("OverlayPanel","overlay22971",{id:"formSmash:j_idt705:0:j_idt709",widgetVar:"overlay22971",target:"formSmash:j_idt705:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Nonlinear localization in discrete and continuum systems: applications for optical waveguide arrays$(function(){PrimeFaces.cw("OverlayPanel","overlay249199",{id:"formSmash:j_idt705:1:j_idt709",widgetVar:"overlay249199",target:"formSmash:j_idt705:1:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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