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。     

Kaup-Kupershmidt方程的非局域对称及新的精确解

利用机械化算法得到了Kaup-Kupershmidt方程的非局域对称、约化,通过解约化方程得到了该方程的一些新的精确解.     

变系数Burgers方程的分类及相似解(英文)

应用经典李群理论考虑了描述非平面冲击波形成和衰减现象的(1 1)维变系数Burgers方程,得到该方程的群分类及相应的对称.对于某些具体形式的色散项系数a(t)和非线性项系数b(t),给出了对应方程的对称约化及相似解.本文在已有基础上给出了方程新的显式解.这些解对于研究某些复杂的物理现象,以及验证数值求解法则的可行性有重要的意义.     

时间分数阶Boussinesq方程的李对称分析

本文利用李群分析方法研究了时间分数阶Boussinesq方程,得到了该方程的李点对称,并把该方程约化为Erdelyi-Kobe分数阶常微分方程. 本文的行文过程也说明了李群分析方法对于约化分数阶非线性发展方程是有效的. 关键词： 李对称分析方法 时间分数阶Boussinesq方程 广义Riemann-Liouville导数 Erdelyi-Kober微分算子     

非线性2+1维Khokhlov-Zabolotskaya方程的无穷多对称及其代数结构

对于2+1维的可积的Khokhlov-Zabolotskaya方程,利用形式级数对称的方法,得到了一包含无穷多任意时间函数的无穷多截断对称。由这些对称构成的无限维李代数是W_(?)代数的推广。 关键词：     

(2+1)维广义Calogero-Bogoyavlenskii-Schiff方程的无穷序列类孤子解

为了构造高维非线性发展方程的无穷序列类孤子新解, 研究了二阶常系数齐次线性常微分方程, 获得了新结论. 步骤一, 给出一种函数变换把二阶常系数齐次线性常微分方程的求解问题转化为一元二次方 程和Riccati方程的求解问题. 在此基础上, 利用Riccati方程解的非线性叠加公式, 获得了二阶常系数齐次线性常微分方程的无穷序列新解. 步骤二, 利用以上得到的结论与符号计算系统Mathematica, 构造了(2+1)维广义Calogero-Bogoyavlenskii-Schiff (GCBS)方程的无穷序列类孤子新解. 关键词： 常微分方程 非线性叠加公式 高维非线性发展方程 无穷序列类孤子新解     

Broer-Kau-Kupershmidt方程组的对称、约化和精确解

利用修正的CK直接方法得到了Broer-Kau-Kupershmidt (简写为BKK)方程组的对称、约化, 通过解约化方程得到了该方程组的一些精确解, 包括双曲函数解、 三角函数解、 有理函数解、 艾里函数解、 幂级数解和 孤立子解等. 关键词： 修正的CK直接方法 BKK方程组 对称、约化 精确解     

(2+1)维离散型Toda方程的对称性

将文献[1—4]提出的形式级数对称理论推广应用到(2+1)维的离散型Toda方程,得到了二族无穷多广义截断对称。每一族对称构成一个广义W_∞代数,通常的W_∞代数仅是这个代数的子代数。 关键词：     

远场模型方程的同伦近似对称约化

以同伦近似对称法为理论依据研究了远场模型方程, 通过归纳各阶相似约化解和各阶相似约化方程的通式构造相应的同伦级数解. 各阶相似约化方程均为线性变系数常微分方程, 并且可以从零阶开始依次求解. 同伦模型中的辅助参数影响同伦级数解的收敛性. 关键词： 同伦近似对称法 远场模型方程 同伦级数解     

Burgers方程新的精确解及初始值问题解的封闭形式

利用扩展齐次平衡法,求出了Burgers方程无穷多个单孤子解和无穷多个有理函数解,特别是得到了Hopf-Cole’s变换和方程初始值问题解的封闭形式.方法简单直接,并且可以推广到其它方程.     

Kac-Moody-Virasoro symmetry algebra of a （2＋1）-dimensional bilinear system

Based on some known facts of integrable models, this paper proposes a new （2＋1）-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable because of the existence of the higher order symmetries. The Lie point symmetries of the model constitute an infinite dimensional Kac- Moody Virasoro symmetry algebra. Making use of the infinite Lie point symmetries, the possible symmetry reductions of the model are also studied     

New interaction solutions and nonlocal symmetry of an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form

The nonlocal symmetry is derived for an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form from the truncated Painlevéexpansion method. The nonlocal symmetries are localized to the Lie point symmetry by introducing new auxiliary dependent variables. The finite symmetry transformation and the Lie point symmetry for the prolonged system are solved directly. Many new interaction solutions among soliton and other types of interaction solutions for the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form can be obtained from the consistent condition of the consistent tanh expansion method by selecting the proper arbitrary constants.     

2+1维双线性Sawada-Kotera方程的对称结构

对一类２＋１维双线性方程从两个不同角度建立了形式级数对称理论。从一已知的时间无关对称出发或从与一维空间坐标有关的任意函数出发，均可得到一包含时间任意函数的形式级数对称。对于２＋１维双线性Ｓａｗａｄａ－Ｋｏｔｅｒａ方程，存在６个截断对称。这些截断对称构成一无穷维李代数。一些有意义的子代数（如Ｖｉｒａｓｏｒｏ代数等）也被给定。     

2＋1维双线性Sawada—Kotera方程的对称结构

对一类２＋１维双线性方程从两个不同程度建立了形式级数对称理论。从一已知的时间无关对称出发或从与一维空间坐标有关的任意函数发出，均可得到了包含时间任意函数的形式级数对称。对于２＋１维双线性Ｓａｗａｄａ－Ｋｏｔｅｒａ方程，存在６个载断对称。这些截断对称构成一无究维李代数。一些有意义的子代数（如Ｖｉｒａｓｏｒｏ代数等）也被给定。     

Soliton solutions and symmetries of the 2+1 dimensional Kaup–Kupershmidt equation

The 2+1 dimensional Kaup–Kupershmidt (KK) equation is considered. A bilinear form for the equation is found and then 3-soliton solutions are obtained with the assistance of Mathematica. Six symmetries of the bilinear 2+1 dimensional KK equation are given and their symmetry algebra is identified.     

Symmetries and conservation laws of one Blaszak–Marciniak four-field lattice equation

In this paper, by using the classical Lie symmetry approach, Lie point symmetries and reductions of one Blaszak– Marciniak(BM) four-field lattice equation are obtained. Two kinds of exact solutions of a rational form and an exponential form are given. Moreover, we show that the equation has a sequence of generalized symmetries and conservation laws of polynomial form, which further confirms the integrability of the BM system.     

A new (2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study

According to the conjecture based on some known facts of integrable models, a new (2+1)-dimensional supersymmetric integrable bilinear system is proposed. The model is not only the extension of the known (2+1)-dimensional negative Kadomtsev--Petviashvili equation but also the extension of the known (1+1)-dimensional supersymmetric Boussinesq equation. The infinite dimensional Kac--Moody--Virasoro symmetries and the related symmetry reductions of the model are obtained. Furthermore, the traveling wave solutions including soliton solutions are explicitly presented.     

Symmetries and symmetry reductions of the combined KP3 and KP4 equation

To find symmetries,symmetry groups and group invariant solutions are fundamental and significant in nonlinear physics.In this paper,the finite point symmetry group of the combined KP3 and KP4(CKP34) equation is found by means of a direct method.The related point symmetries can be obtained simply by taking the infinitesimal form of the finite point symmetry group.The point symmetries of the CKP34 equation constitute an infinite dimensional KacMoody-Virasoro algebra.The point symmetry invariant so...     

Study on a General Hopf Hierarchy

By using a general symmetry theory related to invariant functions,strong symmetry operators and hereditary operators,we find a general integrable hopf heirarchy with infinitely many general symmetries and Lax pairs.For the first order Hopf equation,there exist infinitely many symmetries which can be expressed by means of an arbitrary function in arbitrary dimensions.The general solution of the first order Hopf equation is obtained via hodograph transformation.For the second order Hopf equation,the Hopf-diffusion equation,there are five sets of infinitely many symmetries.Especially,there exist a set of primary branch symmetry with which contains an arbitrary solution of the usual linear diffusion equation.Some special implicit exact group invariant solutions of the Hopf-diffusion equation are also given.     

Conservation laws of the complex short pulse equation and coupled complex short pulse equations

In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models are turned into multi-component real models by proper transformations. Lie symmetries are obtained via the classical Lie group method, and the results for the coupled complex short pulse equations contain the existing results as particular cases. Based on the linearizing operator and adjoint linearizing operator for the two real systems, adjoint symmetries can be obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair (SA) method. Relationships between the nonlinear self-adjointness method and the SA method are investigated.