给出并证明了薛定谔方程中高斯包络孤子的表达式.针对该高斯包络孤子进一步提出了薛定谔方程中存在高斯包络孤子相互作用的情况;针对薛定谔方程提出其辛算法.通过分离波函数实部和虚部把薛定谔方程变换成标准的哈密顿正则方程组,对正则方程进行欧拉中心差分离散实现辛算法.给出了辛算法的守恒量,并证明了其稳定性.对薛定谔方程中的高斯包络孤子运动及多孤子相互作用过程进行了数值仿真,实验结果证明了所提观点的正确性及辛算法的有效性.
The expression of Gaussian envelope solitonin SchrSdinger equation is given and proved.According to the Gaussian envelope soliton,Gaussian envelope soliton interaction situation existing in Schr(o)dinger equation is further proposed.The symplectic algorithm for solving Schr(o)dinger equation is proposed.The Schr(o)dinger equation is transformed into the standard Hamiltonian canonical equation by separating the real and imaginary parts of wave function,and the symplectic algorithm is implemented by using Euler center difference separation for the canonical equation.The conserved quantity of symplectic algorithm is given,and its stability is proved.The numerical simulation is carried out on Gaussian envelope soliton motion and multi-soliton interaction in Schr(o)dinger equation.Experimental results prove the correctness of the proposed method and validity of symplectic algorithn.
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