推广的Boussinesq方程和KdV方程——Painlevé性质,Bcklund变换和Lax对

本文从Kadomtsev-Petviashvili方程的对称性约化出发,得到了具有任意函数作为变系数的推广的Boussinesq方程和推广的KdV方程.利用Weiss和Kruskal等建立的奇性分析方法,我们证明了这两个方程可积的充分条件:Painlevé性质。得到了这两个方程的Bcklund变换和奇性流形方程(推广的Schwartz-Boussinesq方程和Schwartz-KdV方程)。并由此将这两个方程线性化,即给出这两个方程的Lax对并包含有明显的与时间无关的任意谱参数。     

Interactions Between Solitons and Cnoidal Periodic Waves of the(2+1)-Dimensional Konopelchenko–Dubrovsky Equation

The(2+1)-dimensional Konopelchenko–Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the(2+1)-dimensional Konopelchenko–Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the(2+1)-dimensional Konopelchenko–Dubrovsky equation is solved by the consistent Riccati expansion(CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the(2+1)-dimensional Konopelchenko–Dubrovsky equation.     

非晶SiO_2薄膜中氧双键缺陷电子及光学特性的第一性原理研究

利用第一性原理对离子溅射沉积的非晶SiO2薄膜微观结构进行了分析、研究,结果表明,氧双键缺陷(SGs)可以作为体缺陷稳定存在于非晶SiO2中,SGs缺陷导致非晶SiO2薄膜材料禁带中引入了新的电子态,减小了禁带宽度;同时采用时相关密度泛函理论(TDDFT)对其光学特性进行了研究,得到非晶SiO2薄膜介电常数与入射光子能量间的关系曲线,从介电常数的虚部发现SGs缺陷在3.6eV处存在一个光学吸收峰.     

非拓扑孤子袋模型的退禁闭相变和φ4场的对称性恢复相变

在Hartree平均场近似和高温近似下,本文建立了φ⁴模型和非拓扑孤子袋模型的某些特解间确定的映射关系,从映射关系我们看到φ⁴场的非球对称拓扑孤子和反孤子配对形成束缚态——孤子袋模型的非球对称非拓扑孤子解.当拓扑孤子和反孤子消失时,φ⁴模型发生对称性恢复相变;当拓扑孤子和反孤子的束缚态非拓扑孤子消失时,孤子袋模型的退禁闭相变发生.     

A Discrete Lax-Integrable Coupled System Related to Coupled KdV and Coupled mKdV Equations

A modified Korteweg-de Vries （mKdV） lattice is found to be also a discrete Korteweg-de Vries （KdV） equation. A discrete coupled system is derived from the single lattice equation and its Lax pair is proposed. The coupled system is shown to be related to the coupled KdV and coupled mKdV systems which are widely used in physics.     

Fractal Solutions of the Nizhnik—Novikov—Veselov Equation

Considering that some types of fractal solutions may appear in many (2 1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions,we use some special types of lower dimensional fractal functions to construct higher dimensional fractal solutions of the Nizhnik-Novikov-Veselov equation.The static eagle-shape fractal solutions,fractal dromion solutions and the fractal lump solutions are given in detail.     

Exact Solutions of Supersymmetric KdV-a System via Bosonization Approach

Bosonization approach is applied in solving the most general N=1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a (sKdV-a) equation. By introducing some fermionic parameters in the expansion of the superfield, the sKdV-a equation is transformed to a new coupled bosonic system. The Lie point symmetries of this model are considered and similarity reductions of it are conducted. Several types of similarity reduction solutions of the coupled bosonic equations are simply obtained for all values of a. Some kinds of exact solutions of the sKdV-a equation are discussed which was not considered integrable previously.     

量子力学混合态表象

在以往的文献中量子力学的表象都是纯态表象,在本文中我们从算符的合理排序和概率统计的正态分布思想出发,首次提出了量子力学混合态表象的概念,并证明了其完备性和正交性.量子力学混合态表象的优点是可以反映算符的多种表示以及其相应的排序规则.     

Searching for Infinitely Many Symmetries and Exact Solutions via Repeated Similarity Reductions

A simple symmetry reduction procedure is repeatedly used to obtain infinitely many symmetries and then the exact solutions of the Burgers equation. Some sets of exact solutions such as the rational solutions, rationalkink solutions and error function solutions are explicitly given. As a byproduct the recursion operators can be re-obtained at the same time.     

耦合Burgers系统的Painlevé性质分析，对称和对称约化

本文给出了耦合Burgers系统的Painlevé性质，逆强对称算子，无穷多对称和李对称约化。通过把强对称和逆强对称算子重复多次作用到耦合Burgers模型的一些平庸对称，如恒等变换，空间平移变换和标度变换上，我们得到了三族无穷多对称。这些对称构成了无穷维李代数。用其中的有限维子代数——点李代数对模型进行对称约化，得到了模型的群不变解。