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Using Lie group theory and canonical transformations we construct explicitsolutions of nonlinear Schrodinger equations with spatially inhomogeneousnonlinearities. We present the general theory, use it to show that localizednonlinearities can support bound states with an arbitrary number solitons anddiscuss other applications of interest to the field of nonlinear matter waves

Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities