The authors show that pulse propagation in a periodic dispersion manag
ed system with an asymmetric dispersion map is distinguished by transi
ent fluctuations. For some dispersion allocations, the transient settl
es after one soliton period into a quasi-stable state provided that th
e soliton energy is optimised. The range of dispersion maps that satis
fies different stability criteria, or that maximises some figure of me
rit, is identified.