摘要
从带有某种扰动项的一般NLS方程出发,采用奇异摄动的方法,得到了方程的零级近似方程和一级近似方程,通过对近似方程中算子的特征态的讨论,引入适当的"导出态",建立了算子在空间的特征态的完备性 利用这种完备性,得到近似方程中相应的量在该完备集中的展开式,并得到展开式中系数的演化方程,再通过对这些演化方程的讨论,求得了该方程在微小扰动下的一级近似解 所得的近似解具有较好的精确性。
Beginning with a perturbed generalized NLS equation by using a singular perturbation expansion method, we obtain the zero order and the first order equations.We then discuss the eigenstates of the operator in the equations and introduce the relevant 'derivative states', so that to form the completeness of the bounded eigenstates of the associated operator in L2 space. We then expand the corresponding quantums in the closure to get a series evolution equations of the coefficients in the expanded formulas. At last we find the first order approximate solution by solving the evolution equations. This method can be used in other NLS equations with any perturbed terms.
出处
《江苏大学学报（自然科学版）》
EI
CAS
2003年第2期92-94,共3页
Journal of Jiangsu University：Natural Science Edition
基金
国家自然科学基金资助项目(100710033)
江苏大学青年基金资助项目(02JDQ013)
关键词
微小扰动
NLS方程
解
奇异摄动
特征态
算子
NLS equation
eigenstate
perturbation
first order approximate solution
