科研之友
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摘要
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 find 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 pi 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 hands 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.
- 出版日期2005-8
