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.

中文翻译：

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非线性薛定谔方程的自适应多分辨率超弱不连续伽辽金方法

本文开发了一种用于求解非线性薛定谔方程的高阶自适应方案。此类方程的解通常表现出孤立波和局部结构，这使得自适应性对于提高模拟效率至关重要。我们的方案使用超弱不连续伽辽金（DG）公式，属于自适应多分辨率方案的框架。提出了各种数值实验，以证明捕获孤子波和爆炸现象的出色能力。