四阶时间分数阶演化方程的Lie对称分析和守恒律（英文）

主要研究了四阶时间分数阶演化方程的Lie对称分析和守恒.基于Lie点对称方法,分别得到了该方程的相关向量场以及相似约化.在相似约化的基础上,通过该方法来获得分数阶常微分方程是非常有效的.最后,通过非线性的自伴随方法和时间分数阶的黎曼-刘维尔导数算子以及欧拉-拉格朗日算子,得到了该方程的守恒律.

耗散量子Zakharov方程的对称约化和守恒律

基于Lie对称分析,利用耦合非线性耗散量子Zakharov方程一维子Lie代数的优化系统完成其相似约化.此外,借助直接(乘子)方法也构造出耗散量子Zakharov方程的守恒律.

Full Symmetry Groups and Similar Reductions of a (2+1)-Dimensional Resonant Davey-Stewartson System

Applying the classical Lie symmetry method to the （29-1）-dimensional resonant Davey-Stewartson system introduced by Tang IX. Y. Tang et al., Chaos, Solitons and Practals 42 （2007） 2707], a more general infinite dimensional Lie symmetry with Kac-Moody-Virasoro type Lie algebra is obtained, which involves four arbitrary functions of t. Alternatively, by a simple direct method, the full symmetry groups including Lie symmetry group and non-Lie symmetry group are gained straightly. In this way, the related Lie algebra can be easily found by a more simple limiting procedure. Lastly, via solving the characteristic equations, three types of the general similar reductions are derived.

Exact Solutions of(2+1)-Dimensional HNLS Equation

In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the （2＋1）-dimensional hyperbolic nonlinear Schr6dinger （HNLS） equation and reduce the （2＋1）-dimensional HNLS equation to some （1 ＋ 1 ）-dimensional partial differential systems. Finally, many exact travelling solutions of the （2＋1）-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method.

A Note on Similarity Reductions of Barotropic and Quasi-geostrophic Potential Vorticity Equation

Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented in a previous work [F. Huang, Commun. Theor. Phys. （Beijing, China） 42 （2004） 903]. A general finite transformation group is obtained based on the full Lie point symmetry, Furthermore, two new types of similarity reduction solutions are obtained.

Symmetry and Exact Solutions of (2+1)-Dimensional Generalized Sasa-Satsuma Equation via a Modified Direct Method

In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmethod proposed by Lou [J. Phys. A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained andthe relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groupsobtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equationsare constructed by the relationship obtained in the paper between the new solution and known solution.

On New Similarity Solutions of the Boiti–Leon–Pempinelli System

In the present work, the new exact solutions of the Boiti-Leon-Pempinelli system have been found. The system has extensive physical background. The exact solutions of the Boiti-Leon-Pempinelli system are investigated using similarity transformation method via Lie group theory. Lie symmetry generators are used for constructing similarity variables for the given system of partial differential equations, which lead to the new system of partial differentiaJ equations with one variable less at each step and eventually to a system of ordinary differential equations （ODEs）. Finally, these ODEs are solved exactly. The exact solutions are obtained under some parametric restrictions. The elastic behavior of the soliton solutions is shown graphically by taking some appropriate choices of the arbitrary functions involved in the solutions.