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This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modul...
The nonlinear propagation of light pulses in liquid-filled photonic crystal fibers is considered. Due to the slow reorientational nonlinearity of some molecular liquids, the nonlinear modes propagatin...
We report the first prediction of fully localized two-dimensional embedded solitons. These solitons are obtained in a quasi-one-dimensional waveguide array which is periodic along one spatial directio...
The stability of dark solitons generated by a supersonic flow of a Bose-Einstein condensate past a concave corner (or a wedge) is studied. It is shown that solitons in the dispersive shock wave genera...
We address the problem of directional mobility of discrete solitons in two-dimensional rectangular lattices, in the framework of a discrete nonlinear Schr\"odinger model with saturable on-site nonline...

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