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The residual symmetries of the Ablowitz–Kaup–Newell–Segur(AKNS)equations are obtained by the truncated Painleve′analysis.The residual symmetries for the AKNS equations are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries of a prolonged AKNS system.The local Lie point symmetries of the prolonged AKNS equations are composed of the residual symmetries and the standard Lie point symmetries,which suggests that the residual symmetry method is a useful complement to the classical Lie group theory.The calculation on the symmetries shows that the enlarged equations are invariant under the scaling transformations,the space–time translations,and the shift translations.Three types of similarity solutions and the reduction equations are demonstrated.Furthermore,several types of exact solutions for the AKNS equations are obtained with the help of the symmetry method and the Bcklund transformations between the AKNS equations and the Schwarzian AKNS equation. 相似文献
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用Newman叠加模型研究了KZnF_3:Cr~(3 )四角对称基态的零场分裂,证实了Zn~(2 )空位和畸变的存在;并指出,空位对晶场的贡献不可忽略。计算得到:KZnF_3:cr~(3 )晶体[0,01]方向的一个F~-配体向Cr~(3 )移动Δ(KZnF_3)=0.0029-0.0043nm。还研究了KMgF_3:Cr~(3 )四角对称的零场分裂,证实实验测得的零场分裂常数D=-0.2167±0.0004cm~(-1),是由于O~(2-)取代了Cr~(3 )最近邻处的一个F~-,形成的CrOF_3基团所产生的;并指出:与Cr~(3 )-O~(2-)轴相垂直的平面上的四个F~-配体,必须向Cr~(3 )-O~(2-)轴收缩δ,零场分裂常数的计算值才能与实验值一致。同时,Cr~(3 )和O~(2-)要相向移动,而Cr~(3 )移动的距离Δ比O~(2-)移动的距离Δ大。 相似文献
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