A numerical solution to the Zakharov-Shabat inverse scattering problem with application to solitary wave propagation in nonlinear optical fibers

Frangos, P

dc.contributor.author	Frangos, P	en
dc.date.accessioned	2014-03-01T01:11:37Z
dc.date.available	2014-03-01T01:11:37Z
dc.date.issued	1996	en
dc.identifier.issn	0030-4018	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11740
dc.subject	Inverse Scattering	en
dc.subject	Inverse Scattering Problem	en
dc.subject	Nonlinear Optics	en
dc.subject	Nonlinear Partial Differential Equation	en
dc.subject	Numerical Solution	en
dc.subject	Satisfiability	en
dc.subject	Solitary Wave	en
dc.subject.classification	Optics	en
dc.subject.other	Asymptotic stability	en
dc.subject.other	Differentiation (calculus)	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Integral equations	en
dc.subject.other	Light reflection	en
dc.subject.other	Light transmission	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Numerical methods	en
dc.subject.other	Optical fibers	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Solitons	en
dc.subject.other	Gelfand-Levitan-Marchenko integral equations	en
dc.subject.other	Nonlinear Schrodinger equation	en
dc.subject.other	Solitary wave	en
dc.subject.other	Zakharov-Shabat inverse scattering problem	en
dc.subject.other	Light scattering	en
dc.title	A numerical solution to the Zakharov-Shabat inverse scattering problem with application to solitary wave propagation in nonlinear optical fibers	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/0030-4018(95)00597-8	en
heal.identifier.secondary	http://dx.doi.org/10.1016/0030-4018(95)00597-8	en
heal.language	English	en
heal.publicationDate	1996	en
heal.abstract	A new numerical solution which uses leapfrogging in space and time is developed in this work in order to solve coupled Gel'fand-Levitan-Marchenko integral equations in their general form, appearing in the formulation of the Zakharov-Shabat coupled-mode inverse scattering problem. As an application, the problem of solitary wave (pulse) propagation in a nonlinear optical fiber is implemented using the method developed here, since the envelope of the propagating solitary wave is found to satisfy the nonlinear (cubic) Schrödinger equation. It is found that the proposed method for the solitary wave calculation, based on the inverse scattering integral formulation, is very efficient and accurate, especially in the late-time period, where traditional methods based on the direct numerical solution of the corresponding nonlinear partial differential equation become inaccurate.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Optics Communications	en
dc.identifier.doi	10.1016/0030-4018(95)00597-8	en
dc.identifier.isi	ISI:A1996UB63600052	en
dc.identifier.volume	123	en
dc.identifier.issue	4-6	en
dc.identifier.spage	743	en
dc.identifier.epage	751	en