Lie symmetries and solitons in nonlinear systems with spatially   inhomogeneous nonlinearities
  Using Lie group theory and canonical transformations we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons and discuss other applications of interest to the field of nonlinear matter waves. 
Juan Belmonte-Beitia, Victor M. Perez-Garcia, Vadym Vekslerchik, Pedro   J. Torres