李志斌
非线性系统中的符号计算问题
个性化签名
- 姓名:李志斌
- 目前身份:
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学术头衔:
博士生导师
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学科领域:
计算机软件
- 研究兴趣:非线性系统中的符号计算问题
李志斌 男, 汉族, 1960年3月生。1988年6月毕业于兰州大学数学系基础数学专业,获理学博士学位。1985年-1999年先后在兰州大学数学系、计算机系任教,2000年调华东师范大学工作,现为华东师范大学计算机科学技术系教授、博士研究生导师,并兼任校学科建设与发展办公室主任。研究方向:非线性系统中的符号计算问题。符号计算是随着计算机科学理论与技术的发展而产生的一种新型计算技术,它主要探讨以符号、公式为对象的算法研究。符号计算方法已经成为解决非线性问题的极为有利的工具。为使这种计算方法在非线性系统这一科学领域发挥出巨大作用,多年来我们在这个研究方向上积极探索,在国内首先开始了非线性偏微分方程精确解的符号计算研究,取得了重要的进展。2000年以来在这个研究领域已经发表SCI论文三十余篇。研究工作得到国家重点基础研究发展规划项目、上海市曙光计划项目、上海市自然科学基金、上海市高等学校科技发展基金以及教育部博士点专项基金的资助。
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1219
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成果数
11
【期刊论文】Synthesis and biological activities of fluorine-containing N,N~-diphenylcarbamimidothioates
李志斌
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-1年11月30日
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引用
李志斌, Shan-qing Zhang, Zhi-bin Li
Acta Mathematicae Applicatae Sinica, English Series Vol. 20, No.4(2004)605-616,-0001,():
-1年11月30日
In this paper, an algorithm for computing the Janet bases of linear differential equations is described, which is the differential analogue of the algorithm JanetBasis improved by Gerdt. An implementation of the algorithm in Maple is given. The implemented algorithm includes some subalgorithms: Janet division, Pommaret division, the judgement of involutive divisor and reducible, the judgement of conventional divisor and reducible, involutive normal form and conventional normal form, involutive autoreduction and conventional autoreduction, PJ-autoreduction and so on. As an application, the Janet Bases of the determining system of classical Lie symmetries of some partial differential equations are obtained using our package.
Involutive bases,, Janet bases,, Gr
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【期刊论文】AN ALGORITHM OF CONSTRUCTING THE CONSERVATION LAWS OF NONLINEAR EVOLUTION EQUATIONS
李志斌, RUO-XIA YAO*, †, ‡, and ZHI-BIN LI*, §
International Journal of Modern Physics B Vol. 18, Nos. 17-19(2004)2633-2639,-0001,():
-1年11月30日
An algorithm of constructing the polynomial type conservation laws of nonlinear evo-lution equations (either parameterized or non-parameterized) is described and a Maple package CONSLAW to automate the computation is presented. For parameterized equa-tion(s), CONSLAW can determine the parameters constraints automatically such that a sequence of conservation laws exist.
Symbolic computation, nonlinear evolution equation, scaling symmetry, conservation law, integrability.,
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李志斌, ZHANG Shan-Qing, LI Zhi-Bin**
Vlo. 21 No.2(2004)223,-0001,():
-1年11月30日
The master equation of a one-dimensional lattice-gas model with order preservation where the occupation probabilities of sites corresponding to Bose statistcs as a consequence of the prescribed dynamics is studied with the potential symmetry method. The infinite-parameter potential symmetry and a new exact solution are obtainde. The result illustrates that there remains the possibility of the above nonlinear equation to a linear partial differential equation by a non-invertible mapping.
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【期刊论文】On New Invariant Solutions of Generalized Fokker Planck Equation*
李志斌, YAO Ruo-Xia, , and LI Zhi-Bin
Commun. Theor. Phys. (Beijing, China) 41(2004) pp. 665-668,-0001,():
-1年11月30日
The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first reported.
Fokker-Planck equation,, potential symmetry,, invariant solutions,, symbolic computation
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【期刊论文】Conservation laws and new exact solutions for the generalized seventh order KdV equation
李志斌, Yao Ruo-Xia a, b, Li Zhi-Bin a, *
Chaos, Solitons and Fractals 20(2004)259-266,-0001,():
-1年11月30日
Abundant polynomial type conservation laws are constructed for a seventh order nonlinear evolution equation with six arbitrary parameters. From the parameters constraints that leading to the existence of conserved densities, a new unnamed seventh order KdV type equation that may be integrable is reported. By introducing nonlinear transformation, the new soliton solution as well as the solitary wave solution to the new unnamed seventh order KdV type equation are obtained.
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【期刊论文】New exact solutions for three nonlinear evolution equations
李志斌, Ruo-xia Yao a, b, Zhi-bin Li a, *
Physics Letters A 297(2002)196-204,-0001,():
-1年11月30日
By using the general solutions of a coupled Riccati equations and the relations between them a direct algebra method is described to construct several kinds of closed-form travelling wave solutions for some nonlinear differential equations. By this method three important nonlinear partial differential equations are studied and, in addition to rederiving all known solutions, several new solutions are explicitly obtained with the aid of symbolic computation.
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引用
李志斌, Gui-qiong Xu a, b, *, Zhi-bin Li a
Computer Physics Communications 161(2004)65-75,-0001,():
-1年11月30日
A software package wkptest written in Maple is presented, which can carry out the traditional Painlev
Nonlinear partial differential equations, Painlev
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引用
李志斌, Zhi-Bin Li*, Yin-Ping Liu
Computer Physics Communications 163(2004)191-201,-0001,():
-1年11月30日
Nature of physical problem: Our program provides exact traveling wave solutions, which describe various phenomena in nature, and thus can give more insight into the physical aspects of problems. These solutions may be easily used in further applications. Restriction on the complesity of the problem: The program can handle system of nonlinear evolution equations with any number of independent and dependent variables, in which each equation is a polynomial (or can be converted to a polynomial) in the dependent variables and their derivatives. Typical running time: It depends on the input equations as well as the degrees of the desired polynomial solutions. For most of the equations we have computed, the running time is no more than 100s. In Maple 8, by taking advantage of the package RIF contained in DEtools, we developed a package RAEEM which is a comprehensive and complete implementation of such methods as the tanh-method, the extended tanh-method, the Jacobi elliptic function method and the elliptic equation method. RAEEM can entirely automatically output a series of exact traveling wave solutions, including those of polynomial, exponential, triangular, hyperbolic, rational, Jacobi elliptic, Weierstrass elliptic type. The effectiveness of the package is illustrated by applying it to a large variety of equations. In addition to recovering previously known solutions, we also obtain more general forms of some solutions and new solutions.
Nonlinear evolution equations, Traveling wave solutions, Dependent variable, Independent variable
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李志斌, Shan-Qing Zhang, Gui-Xu Zhang, Zhi-Bin Li*
Applied Mathematics and Computation xxx(2004)xxx-xxx,-0001,():
-1年11月30日
A constructive algorithm for the completion of arbitrary algebraic partial differential equation systems to involutive ones are presented. Based on it, an implementation ICS for computing the involutive characteristic set of an algebraic partial differential equation systems is given. Some examples are tested with ICS and some experimental results are obtained which may show a hint for computing involutive characteristic set of arbitrary algebraic partial differential equation systems thereafter.
Partial differential equations, Involutive characteristic set, Symbolic computation
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