Higher-order quasi-solitons of an adapted dispersion profile

Some years ago, Tajima [1] suggested that the solitonic balance between nonlinearity and dispersion could be maintained in a lossy fiber by a proper (exponential) tailoring of the dispersion profile. Since then, the idea has been generalized to include higher-order effects [2]. More recently, Kumar and Hasegawa [3] introduced the concept of " quasi-soliton ", a chirped soliton adapted to a novel dispersion profile. The pre-chirping of the input soliton has the advantage of limiting the emission of radiation and reducing the pulse interaction [4]. In this paper, we discuss of the existence of higher-order quasi-solitons that can propagate along the same dispersion profile with the same evolution of their parameters. Analytical expressions are presented for the pulse shapes, as well as the appropriate grating parameter required for long-haul transmission.