Abstract
A brief review of basic models describing second harmonic generation (SHG) in dispersive and diffractive optical systems,and of fundamental soliton solutions to these models is given. Included are two- and three-wave models, gap solitons, linearly coupled waveguides with an intrinsic quadratic nonlinearity,m ultidimensional “light bullets”, two-soliton bound states (which are always unstable in the usual SHG models,but may be stable in the SHG models that give rise to gap solitons),and modulational instability of cw states. Both analytical results,obtained by means of the variational approximation (VA),and numerical results are presented. In practically all the cases,V A demonstrates a fairly good agreement with direct simulations.
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