Classification and Approximate Solutions to a Class of Perturbed Nonlinear Wave Equations

A complete approximate symmetry classification of a class of perturbed nonlinear wave equations is performed using the method originated from Fushchich and Shtelen. Moreover, large classes of approximate invariant solutions of the equations based on the Lie group method are constructed.     

Modified Boussinesq System with Variable Coefficients： Classical Lie Approach and Exact Solutions

The Lie-group formalism is applied to investigate the symmetries of the modified Boussinesq system with variable coefficients. We derived the infinitesimals and the admissible forms of the coefficients that admit the classical symmetry group. The reduced systems of ordinary differential equations deduced from the optimal system of subalgebras are further studied and some exact solutions are obtained.     

Lie Group Classifications and Non-differentiable Solutions for Time-Fractional Burgers Equation

Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained.     

三类随机系统广义概率密度演化方程的解析解

近年来逐步发展的概率密度演化方法理论为随机动力系统的分析与控制研究提供了新的途径.过去若干年来,已经发展了一系列数值方法如有限差分法、无网格法用于求解广义概率密度演化方程.但是,针对典型随机系统,关于这一方程解析解尚比较缺乏.本文以李群方法为工具,研究给出了Van der Pol振子、Riccati方程和Helmholtz振子3类典型随机非线性系统的广义概率密度演化方程解析解.这些结果,不仅可以作为检验求解广义概率密度演化方程的数值方法结果正确性的判别依据,也为概率密度演化理论的进一步深入研究提供了若干分析实例.      

Symmetries of boundary layer equations of power-law fluids of second grade

A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.     

饱和土体自重固结问题的相似解

采用了比以往更为普遍的土体物理力学性质假设,利用Hopf-Cole变换方法求得了厚层土体在自重应力作用下的非线性固结问题的完整解析解答．通过试验数据,将该解答与传统的大应变线性固结理论解答和基于实验数据的有限元数值解答相比较,结果表明,该解答能够更好地描述土体的实际固结过程,而由线性化固结理论所得的解答对固结过程中的沉降量和固结度的估计偏小．     

关于完备李群与完备李代数

孟道骥等对完备李代数作了系统的研究并已获得很多基本和重要的结果。本文给出完备李群与完备李代数的某些关系。     

DISTORTION THEOREM FOR BIHOLOMORPHIC MAPPINGS IN TRANSITIVE DOMAINS （Ⅳ）

The distortion theorem for biholomorphic starlike mappings (with respect to origin )in bounded symmetric domains are given,The distortion theorem for locally biholomorphic convex mappings in bounded symmetric domains are given also.     

正规李群上BMO函数的分解

本文将在正规李群上建立 BMO 函数的 Fefferman-Stein 分解.