非零远场条件下非线性薛定谔方程的数值模拟

NUMERICAL METHOD FOR COMPUTING ROGUE WAVE IN NONZERO FAR FIELD

针对非零远场条件下非线性薛定谔方程的怪波问题,本文给出了一种有效的Crank-Nicolson差分方法.根据远场渐近行为,设定合理的人工边界条件,给出了在该边界条件下质量和能量的定义式,理论上证明了数值格式对质量和能量的守恒.最后,数值算例说明了该格式具有时空二阶精度,同时验证了质量和能量守恒.

We present an efficient numerical method which is Crank-Nicolson difference method for computing rogue wave of nonlinear Schrodinger equation in nonzero far field. Based on the far field asymptotic behavior, we design reasonable artificial boundary conditions, define the modified mass and energy and prove that the modified mass and energy are conserved. At last, Numerical examples show that the method is second-order accurate in both space and time and conserves the mass and energy in discrete level.