Propagation of Pereira±Sten¯o type pulses in a dispersion varying link: variational approach Manos Manousakis, Panagiotis Papagiannis, Nikos Moshonas, Kyriakos Hizanidis * Department of Electrical and Computer Engineering, National Technical University of Athens, 9 Iroon Polytexniou, 157 73 Athens, Greece Received 20 April 2001; received in revised form 24 July 2001; accepted 28 August 2001 Abstract The evolution during propagation of a Pereira±Sten¯o type bright and chirped) solitary pulse subjected to dis- persion modulation in a communication line with Er 3 -doped ®ber ampli®ers is investigated on the basis of a varia- tionaleectiveparticlemodel.Themodelleadstoanextendedphaseplanerepresentationofthedynamicsofthepulse andyieldstheevolutionequationsforthepulsewidthandchirp.TheassociatedPoincaresurfacesofsectionprovidea usefulqualitativeandquantitativedesigningtoolforasoliton-basedopticallinkwithweaktomildlystrongdispersion modulation. The investigation relates the general properties of the evolution to the modulation strength and its spatial periodicity. Both the sinusoidal and the step-wise dispersion modulation schemes are considered. For the sinusoidal, both weak and relatively strong dispersion modulation, it was found that for long periodicity of the modulation as compared with the periodicity which characterizes the non-modulated breathing of the pulse), chaotic regions on the Poincare surfaces of section are either absent or limited and the pulse preserves its form for adequately long distances for a wide range of choices of its initial parameter values. On the contrary, the higher the modulation strength and/or frequencyarethewiderthechaoticregiongets.Forthecaseofthestep-wisedispersionmodulationthechaoticbehavior setsinforlowervaluesofthefrequencyofthedispersionmodulation,thus,rendingtheregionsforchoosingtheinitial pulse parameters, which are associated with non-destructive propagation of the pulse, narrower. Ó 2001 Published by Elsevier Science B.V. Keywords: EDFAs; Pereira±Sten¯o solitons; Dispersion management; Variational approach; Soliton propagation; Phase-plane dynamics; Chaotic vs. regular motion 1. Introduction Thelastfewyearstherehasbeenaconsiderable amountofresearchworkaswellasofexperiments on designing long haul and high-bit-rate ®ber systems with periodic optical ampli®cation for data transmission based on solitons. Er 3 -doped ®ber ampli®ers EDFAs) [1,2] can usually com- pensate the losses, which are inevitably present in the ®bers. However, optical ampli®ers give rise to various instabilities and related detrimental eects, the most serious one being a random jitter of the solitons induced by their interaction with the optical noise generated by the ampli®er [3]. 1 November 2001 Optics Communications 198 2001) 351±367 www.elsevier.com/locate/optcom * Corresponding author. Fax: +30-1-772-3513. E-mail address: kyriakos@central.ntua.gr K. Hizanidis). 0030-4018/01/$ - see front matter Ó 2001 Published by Elsevier Science B.V. PII:S0030-401801)01527-9