An Adaptive Multiresolution Ultra-weak Discontinuous Galerkin Method for Nonlinear Schrödinger Equations

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