双调和非线性SchrÖdinger方程的低正则算法

Low-Regularity Integrator for the Biharmonic NLS Equation

本文研究了双调和非线性SchrÖdinger方程的具有一阶收敛的一种低正则算法, 得到的算法在损失三阶导数的前提下可以达到一阶收敛. 同时, 我们通过严格的误差分析, 证明了当初值属 于Hγ+3(Td)时, 双调和非线性SchrÖdinger方程在Hγ(Td)上具有一阶收敛, 其中。

In this paper, we introduce a first order low-regularity integrator for the biharmonic nonlinear SchrÖdinger equation. It only requires the boundedness of three additional derivatives of the solution to be the first order convergent. By rigorous error analysis, we show that the scheme provides first order accuracy in Hγ(Td) for rough initial data in Hγ+3(Td) with .