Block （or Hamiltonian） Lie Symmetry of Dispersionless D-Type Drinfeld-Sokolov Hierarchy

In this paper, the dispersionless D-type Drinfeld-Sokolov hierarchy, i.e. a reduction of the dispersionless two-component BKP hierarchy, is studied. The additional symmetry flows of this hierarchy are presented. These flows form an infinite-dimensional Lie algebra of Block type as well as a Lie algebra of Hamiltonian type.     

On the Generalized Heisenberg Supermagnetic Model

In this paper, we construct the generalized Heisenberg supermagnetic models with two different constraints and investigate the integrability of the super integrable systems. By virtue of the gauge transformation, their corresponding gauge equivalent counterparts are derived, i.e., the super and fermionic mixed derivative nonlinear Schrödinger equations, respectively.     

合理开发可再生资源的向量微分模型及其应用

本文首先建立了接年龄分组的可再生资源，各年龄组数量应满足的向量微分模型．然后利用所建模型成功地解决了CMCM96A题中的问题2。     

复数比的定比分点公式与应用

建立复平面后,平面内线段的定比分点公式可以用复数形式来表示,即: 但由于这一公式的应用范围的局限性,本文将考虑更一般的结果,即探讨复平面内复比的定比分点公式与应用。定义设复平面上一点P,它与已知点P_1、P_2构成     

Nonlinear waves of the Hirota and the Maxwell Bloch equations in nonlinear optics

In this paper, considering the Hirota and the Maxwell-Bloch (H-MB) equations which are governed by femtosecond pulse propagation through a two-level doped fiber system, we construct the Darboux transformation of this system through a linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions (both bright and dark breathers) of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.     

THE RECURSION OPERATOR FOR A CONSTRAINED CKP HIERARCHY

This paper gives a recursion operator for a 1-constrained CKP hierarchy, and by the recursion operator it proves that the 1-constrained CKP hierarchy can be reduced to the mKdV hierarchy under condition q = r.     

BKP 与CKP 可积系列的递归算子

借助于新引进的算子B, 本文给出了BKP 与CKP 可积系列约束条件在其Lax 算子L中的动力学变量上的具体体现, 即奇数阶动力学变量u_2k+1 能被偶数阶动力学变量u_2k 显式表达. 同时本文给出了BKP 与CKP 可积系列的流方程以及(2n + 1)- 约化下递归算子的统一公式, 揭示了BKP 可积系列和CKP 可积系列的重要区别. 作为例子, 本文给出了BKP 与CKP 可积系列在3- 约化下的递归算子的显式表示, 并验证了u₂ 的t₁ 流通过递归算子的确可以产生u₂ 的t₇ 流, 该流方程与3- 约化下产生的对应流方程是一致的.     

On the investigation of nonlinear waves of the Hirota and the Maxwell–Bloch equation in nonlinear optics

In this paper, considering the Hirota and Maxwell-Bloch (H-MB) equations which is governed by femtosecond pulse propagation through two-level doped fibre system, we construct the Darboux transformation of this system through linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions (both bright and dark breathers) of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.