Painleve Analysis and Abundant Meromorphic Solutions of a Class of Nonlinear Algebraic Differential Equations

Gu Yongyi; Zheng Xiaoxiao; Meng Fanning

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Painleve Analysis and Abundant Meromorphic Solutions of a Class of Nonlinear Algebraic Differential Equations

机译：一类非线性代数微分方程的Painleve分析和亚纯解

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In this paper, a class of nonlinear algebraic differential equations (NADEs) is studied. The Painleve analysis of the NADEs is considered. Abundant meromorphic solutions of the NADEs are obtained by means of the complex method. Then, meromorphic exact solutions of the Schamel-Korteweg-de Vries (S-KdV) equation and (2+1)-dimensional sine-Gordon equation are derived via the applications of the NADEs.

机译：本文研究了一类非线性代数微分方程（NADE）。考虑了NADE的Painleve分析。通过复杂的方法获得了NADE的丰富亚纯解。然后，通过NADE的应用，推导了Schamel-Korteweg-de Vries（S-KdV）方程和（2 + 1）维正弦-Gordon方程的亚纯精确解。

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《Mathematical Problems in Engineering》 |2019年第4期|9210725.1-9210725.11|共11页
作者
Gu Yongyi; Zheng Xiaoxiao; Meng Fanning;
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Guangdong Univ Finance & Econ, Sch Math & Stat, Guangzhou 510320, Guangdong, Peoples R China|Guangdong Univ Finance & Econ, Big Data & Educ Stat Applicat Lab, Guangzhou 510320, Guangdong, Peoples R China;

Qufu Normal Univ, Sch Math Sci, Qufu 273155, Peoples R China;

Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China;

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1. Painleve Analysis and Abundant Meromorphic Solutions of a Class of Nonlinear Algebraic Differential Equations [J] . Gu Yongyi, Zheng Xiaoxiao, Meng Fanning Mathematical Problems in Engineering . 2019,第PTa4期

机译：一类非线性代数微分方程的痛苦分析和丰富的纯释放解
2. Painlevé Analysis and Abundant Meromorphic Solutions of a Class of Nonlinear Algebraic Differential Equations [J] . Yongyi Gu, Xiaoxiao Zheng, Fanning Meng Mathematical Problems in Engineering: Theory, Methods and Applications . 2019,第1期

机译：一类非线性代数微分方程的PAINLEVÉ分析和丰富的纯释放解决方案
3. MEROMORPHIC SOLUTIONS OF A CLASS OF ALGEBRAIC DIFFERENTIAL EQUATIONS RELATED TO PAINLEVE EQUATION III [J] . Gu Yongyi, Aminakbari Najva, Yuan Wenjun, Houston Journal of Mathematics . 2017,第4期

机译：与痛苦方程III相关的一类代数微分方程的纯释放溶液
4. MEROMORPHIC SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS AND α- YOSHIDA FUNCTIONS [C] . Hasi WULAN ISAAC congress . 2000

机译：代数微分方程和α-yoShida功能的纯纯解
5. Painleve analysis, Lie symmetries and integrability of nonlinear ordinary differential equations. [D] . Lu, Yixia. 2005

机译：非线性常微分方程的Painleve分析，Lie对称性和可积性。
6. One class of meromorphic solutions of general two-dimensional nonlinear equations connected with the algebraic inverse scattering method [O] . D. V. Chudnovsky 1978

机译：一类一般的二维非线性方程的亚纯解与代数逆散射法联系起来
7. Rational transformations of confluent hypergeometric equations and algebraic solutions of the Painleve equations : P1 to P5(Algebraic, Analytic and Geometric Aspects of Complex Differential Equations and their Deformations. Painleve Hierarchies) [O] . Ohyama Yousuke 2007

机译：融合超几何方程的有理变换和Painleve方程的代数解：P1到P5（复微分方程的代数，解析和几何方面及其变形。Painleve层次结构）
8. Meromorphic Solutions of Generalized Algebraic Differential Equations [R] . Yang, C. C. 1971

机译：广义代数微分方程的亚纯解

Painleve Analysis and Abundant Meromorphic Solutions of a Class of Nonlinear Algebraic Differential Equations

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