  This paper develops a high order adaptive scheme for solving nonlinear
Schrodinger equations. The solutions to such equations often exhibit solitary
wave and local structures, which makes adaptivity essential in improving the
simulation efficiency. Our scheme uses the ultra-weak discontinuous Galerkin
(DG) formulation and belongs to the framework of adaptive multiresolution
schemes. Various numerical experiments are presented to demonstrate the
excellent capability of capturing the soliton waves and the blow-up phenomenon.
