Bistable Solitons in Single- and Multichannel Waveguides with the Cubic-Quintic Nonlinearity

ISSN： 0040-5779

Source： Theoretical and Mathematical Physics, Vol.144, Iss.2, 2005-08, pp. : 1157-1165

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

We consider spatial solitons in a channel waveguide or in a periodic array of rectangular potential wells (the Kronig-Penney (KP) model) in the presence of the uniform cubic-quintic (CQ) nonlinearity. Using the variational approximation and numerical methods, we. nd two branches of fundamental (single-humped) soliton solutions. The soliton characteristics, in the form of the integral power Q (or width w) vs. the propagation constant k, reveal a strong bistability with two different solutions found for a given k. Violating the known Vakhitov-Kolokolov criterion, the solution branches with dQ/dk > 0 and dQ/dk < 0="" are="" simultaneously="" stable.="" various="" families="" of="" higher-order="" solitons="" are="" also="" found="" in="" the="" kp="" version="" of="" the="" model:="" symmetric="" and="" antisymmetric="" double-humped="" solitons,="" three-peak="" solitons="" with="" and="" without="" the="" phase="" shift="" ="" between="" the="" peaks,="" etc.="" in="" a="" relatively="" shallow="" kp="" lattice,="" all="" the="" solitons="" belong="" to="" the="" semi-infinite="" gap="" beneath="" the="" linear="" band="" structure="" of="" the="" kp="" potential,="" while="" finite="" gaps="" between="" the="" bands="" remain="" empty="" (solitons="" in="" the="" finite="" gaps="" can="" be="" found="" if="" the="" lattice="" is="" much="" deeper).="" but="" in="" contrast="" to="" the="" situation="" known="" for="" the="" model="" combining="" a="" periodic="" potential="" and="" the="" self-focusing="" kerr="" nonlinearity,="" the="" fundamental="" solitons="" fill="" only="" a="" finite="" zone="" near="" the="" top="" of="" the="" semi-infinite="" gap,="" which="" is="" a="" manifestation="" of="" the="" saturable="" character="" of="" the="" cq="" nonlinearity.="">