二阶非线性SchrÖdinger方程的低正则算法

Low-Regularity Integrator for the Quadratic NLS Equation

本文研究二次非线性SchrÖdinger方程具有一阶收敛的一种低正则积分器,这种积分器是显式的并且快速有效。 特别地,我们的算法不需要损失额外的导数就可以实现一阶收敛。 通过严格的误差分析,我们证明了当初值属于Hγ (T) 时,二次非线性SchrÖdinger方程在Hγ (T)上具有一阶收敛,其中γ > ½。

In this paper, we introduce a first order low-regularity integrator for the quadratic nonlinear SchrÖdinger equation. The scheme is explicit and efficient to implement. In particular, our scheme does not cost any additional derivative for the first order convergence. By rigorous error analysis, we show that the scheme provides first order accuracy in Hγ (T) for rough initial data in Hγ (T) with γ > ½.