Exact solutions in coupled nonlinear Schrödinger equations with spacial inhomogeneous nonlinearity

Abstract:
Using Lie group theory we construct explicit solutions of coupled nonlinear Schrödinger systems with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number of solitons. Their linear and dynamical stability will be investigated as well as we will propose also some applications to the field of nonlinear matter waves.