Qualitative theory of bright solitons: the soliton sketch

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Abstract
Using intuitive physics, we show how to read the stability and the qualitative characteristics of all self-guided (bounded) beams directly from the graph of refractive index versus intensity that characterizes any nonlinear medium. Our approach predicts new soliton classes. It reveals important differences between solitons of one and two transverse dimensions. It links the physical characteristics of solitons and their possible multistabilities directly with topological features of the material nonlinearity n(I). The soliton sketch is introduced as a physical alternative to the usual bifurcation diagrams.