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Spatial control of the competition between self-focusing and self-defocusing nonlinearities in one- and two-dimensional systems
We introduce a system with competing self-focusing (SF) and self-defocusing (SDF) terms, which have the same scaling dimension. In the one-dimensional (1D) system, this setting is provided by a combination of the SF cubic term multiplied by the delta function $\ensuremath{\delta}(x)$ and a spatially uniform SDF quintic term. This system …