Threshold of global existence for 3-D attractive nonlinear Schrödinger equations under confined potentials

Based on a nonlinear critical index, a threshold of global existence on the L2-norm of initial data for 3-D attractive nonlinear Schrödinger equations under confined potentials is derived. For numerical verification, a newly developed radial basis function method is applied in this paper to solve the related nonlinear scalar field equation in R3