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代数微分方程与正规族理论中若干问题研究

项目来源

广东省科技计划

项目主持人

林剑鸣

项目受资助机构

广州中医药大学

立项年度

2015

立项时间

未公开

项目编号

2015A030313346

研究期限

未知 / 未知

项目级别

省级

受资助金额

10.00万元

学科

其他

学科代码

未公开

基金类别

广东省自然科学基金—面上项目

关键词

代数微分方程 ; 正规族理论 ; algebraic differential equation ; Formal family theory

参与者

袁文俊

参与机构

广州大学

项目标书摘要：2010年以来,N.A.Kudryashov等分别对多类数理方程和复的自治常微分方程的精确解进行研究，得到了一部分亚纯解的结果。然而，我们发现对于很多数理方程组以及有应用性物理意义的偏微分方程组，运用复化法研究的还是不多。因此，研究对于许多有物理背景的高阶数理方程以及偏微分方程组如经适当变量替换复化后都可探讨其亚纯解的存在性与表现形式。及在得出解的形式后，我们将进一步分类研究并给出大量数理方程组显式精确解，运用相关数学软件进行演算来确定新的解并绘制函数解的三维动画图形，以便更好研究解的性质。本项目所研究的内容一部分是跨学科、跨方向的问题，一部分是对原有领域相关问题的继续深入。特别是若能在有应用的工程、物理背景意义下的数理方程组经适当变量替换后，探讨非线性微分方程亚纯解的存在性与表示形式以及代数微分方程增长性的估计的问题中有所突破。

Application Abstract: Since 2010,n.a.Kudryashov et al.have studied the exact solutions of multiple mathematical equations and complex autonomous ordinary differential equations respectively,and obtained the results of partial meromorphic solutions.However,we find that for many mathematical equations and partial differential equations with practical physical meaning,the application of the complex method is still rare.Therefore,many high order mathematical equations with physical background and partial differential equations,such as the existence and representation of their meromorphic solutions,can be studied after proper variable substitution and complex.And after we get the solution form,we will further classify and study and give a large number of explicit and accurate solutions of mathematical equations,The related mathematical software performs the calculation to determine the new solution and draw the 3d animation graph of the function solution,so as to study the solution better Properties.Part of the research content of this project is interdisciplinary and cross-directional problems,and Part of it is to continue to deepen the problems in the original field.Especially if can application in engineering,physical significance under the background of mathematical equations after appropriate variable substitution,discusses the existence of meromorphic solutions of nonlinear differential equation and representation,and the growth of algebraic differential equation estimation problem of a breakthrough.

项目受资助省

广东省

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  • 1.Normality and Shared Values of Meromorphic Functions with Differential Polynomial

    • 关键词：
    • ;Differential polynomial;Meromorphic function;Normal family;Uniformly convergence;Zeros
    • Cui, Li-Xia;Yuan, Wen-Jun
    • 《9th International Conference on Fuzzy Information and Engineering, ICFIE 2017》
    • 2019年
    • July 20, 2017 - July 25, 2017
    • Huhehaote, China
    • 会议

    In this paper, we discuss the normality and shared values of meromorphic functions with differential polynomial. We obtain the main result: Let F be a family of meromorphic functions in a domain D and k, q be two positive integers. Let P(z, w) = wq+ aq-1(z) wq-1+ &mellip; + a1(z) w and H(f, f′, …, f(k)) be a differential polynomial with Γγ|H © 2019, Springer Nature Switzerland AG.

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  • 2.Non-traveling wave exact solutions of (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation

    • 关键词：
    • Lie groups;(3+1)-Dimensional Yu-Toda-Sasa-Fukuyama equation;Elliptic functions;Exact wave solutions;Lie group method;Meromorphic function;Non-traveling waves;Reduced equations;Traveling wave
    • Aminakbari, Najva;Dang, Guo-Qiang;Gu, Yong-Yi;Yuan, Wen-Jun
    • 《International Conference on Mathematics and Decision Science, ICMDS 2016》
    • 2018年
    • September 12, 2016 - September 15, 2016
    • Guangzhou, China
    • 会议

    In this paper, the exact solutions for (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation have been investigated. By Lie group method and traveling wave transformation, we obtain two symmetry reduced equations of (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation. Then three classes of non-traveling wave exact solutions of (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation are constructed. At last, we achieve some computer simulations to illustrate our main results. © Springer International Publishing AG 2018.

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