约束离散KP方程族的完全Virasoro对称

首先讨论了约束离散KP可积方程族一种等价形式:差分算子的商.接下来,利用这种新的描述形式,构造了约束离散KP方程族的完全Virasoro对称.     

Squared Eigenfunction Symmetries for the BTL and CTL Hierarchies

In this paper, the squared eigenfunction symmetries for the BTL and CTL hierarchies are explicitly constructed with the suitable modification of the ones for the TL hierarchy, by considering the BTL and CTL constraints. Also the connections with the corresponding additional symmetries are investigated: the squared eigenfunction symmetry generated by the wave function can be viewed as the generating function for the additional symmetries.     

Dynamics of the Smooth Positons of the Wadati-Konno-Ichikawa Equation

We discuss a modified Wadati-Konno-Ichikawa(m WKI) equation,which is equivalent to the WKI equation by a hodograph transformation.The explicit formula of degenerated solution of m WKI equation is provided by using degenerate Darboux transformation with respect to the eigenvalues,which yields two kinds of smooth solutions possessing the vanishing and nonvanishing boundary conditions respectively.In particular,a method for the decomposition of modulus square is operated to the positon solution,and the approximate orbits before and after collision of positon solutions are displayed explicitly.     

Degenerate Solutions of the Nonlinear Self-Dual Network Equation

The N-fold Darboux transformation(DT) T_n~([N]) of the nonlinear self-dual network equation is given in terms of the determinant representation. The elements in determinants are composed of the eigenvalues λ_j(j = 1, 2..., N)and the corresponding eigenfunctions of the associated Lax equation. Using this representation, the N-soliton solutions of the nonlinear self-dual network equation are given from the zero "seed" solution by the N-fold DT. A general form of the N-degenerate soliton is constructed from the determinants of N-soliton by a special limit λ_j →λ_1 and by using the higher-order Taylor expansion. For 2-degenerate and 3-degenerate solitons, approximate orbits are given analytically,which provide excellent fit of exact trajectories. These orbits have a time-dependent "phase shift", namely ln(t~2).     

自旋1／2和自旋1系统在一维变化磁场中的精确解和Aharonov－Anandan相

本文首先根据Ｍｉｚｒａｈｉ构造不变量的方法建立了在一维变化磁场中自旋ｊ系统的不变量，然后利用自旋１／２和自旋１系统不变量的简明矩阵形式直接求解不变量的本征波函数，由此给出了该系统含时Ｓｃｈｒｏｄｉｎｇｅｒ方程的精确解，进而根据Ｌｅｗｉｓ相讨论了此系统的Ａｈａｒｏｎｏｖ－Ａｎａｎｄａｎ相。     

量子代数SU_（qs）（2）和SU_（qs）（1，1）的广义qs－玻色实现

本文给出了双参数形变量子代数ＳＵｑｓ（２）和ＳＵｑｓ（１，１）的Ｈｏｌｓｔｅｉｎ－Ｐｒｉｍａｋｏｆｆ实现的明显形式。此外，通过引入广义ｑｓ－玻色算符，得到了Ｈｏｌｓｔｅｉｎ－Ｐｒｉｍａｋｏｆｆ实现的多ｑｓ－玻色子形式。     

双参数形变谐振子湮灭算符二次幂的本征态

本文明显构造了双参数形变谐振子湮灭算符二次幂的本征态，并利用ｑｓ－积分给出了其完备性的证明。     

qs－超对称振子及其qs－超代数

本文引入了ｑｓ－费米振子的概念，然后构造了ｑｓ－超对称振子，并给出其相应的ｑｓ－超代数的实现．此外，我们给出了双参数形变量子代数ＳＵ_（ｑｓ）（２）的ｑｓ－费米振子实现．     

双参数变谐振子湮灭算符高次幂的本征态

明显构造了双参数ｑｓ－形变谐振子湮灭算符高次幂的本征态，并利用ｑｓ－积分给出了其完备性证明。     

空间位移PT对称非局域非线性薛定谔方程的高阶怪波解

利用Kadomtsev-Petviashvili(KP)系列约束方法和双线性方法,构造了空间位移宇称-时间反演(PT)对称非局域非线性薛定谔方程的高阶怪波解.任意N阶怪波解的解析表达式是通过舒尔多项式表示的.首先通过分析一阶怪波解的动力学行为,发现怪波的最大振幅可以大于背景平面三倍的任意高度.分析了对称非局域非线性薛定谔方程中的空间位移因子x₀在一阶怪波解中的影响,结果表明其仅改变怪波中心的位置.另外,研究了二阶怪波解的动力学行为以及怪波模式,然后给出了N阶怪波模式与N阶怪波解的解析表达式中参数之间的关系,进一步展示了高阶怪波的不同模式.