非线性Schrödinger方程几类孤立子解:局部间断Petrov-Galerkin方法

Several Kinds of Soliton Solution of Nonlinear Schrödinger Equation:Local Discontinuous Petrov⁃Galerkin Method

构造一类求解非线性薛定谔方程的局部间断Petrov-Galerkin方法。利用构造的方法模拟几种类型的孤立子并讨论与孤立子密切相关的一些现象,包括孤立子的传播与碰撞,动孤立子和驻孤立子的生成,N孤立子的有界态。该方法可以模拟孤立子相关现象中一些复杂结构。数值实验表明该方法具有高阶精度且可以达到最优收敛阶。局部间断Petrov-Galerkin方法的计算效率与局部间断Galerkin方法相当,但计算公式简单。

A local discontinuous Petrov⁃Galerkin method is developed for nonlinear Schrödinger equations.Several kinds of solitons are simulated and related phenomena are discussed,such as the soliton propagation and collision,birth of solitons including standing soliton and mobile soliton,the bound state of N solitons.The algorithm simulates some narrow structures in soliton related phenomenon.Numerical examples show that the algorithm has high accuracy and can reach the optimal convergence order.Compared with local discontinuous Galerkin method,the local discontinuous Petrov⁃Galerkin method has high computational efficiency and simple computational formula.