New exact solutions for the Konopelchenko-Dubrovsky equation using an extended Riccati equation rational expansion method and symbolic computation

Song L; Zhang HQ

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New exact solutions for the Konopelchenko-Dubrovsky equation using an extended Riccati equation rational expansion method and symbolic computation

机译：使用扩展的Riccati方程有理展开方法和符号计算的Konopelchenko-Dubrovsky方程的新精确解

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In this paper, based on computerized symbolic computation and a new general ansatz, an extended Riccati equation rational expansion method is presented to construct multiple exact solutions for nonlinear evolution equations and implemented in a computer algebraic system. The validity and reliability of the method are tested by its application to the Konopelchenko-Dubrovsky equation. The method can be applied to other nonlinear evolution equations in mathematical physics. (c) 2006 Published by Elsevier Inc.

机译：本文基于计算机符号计算和一种新的通用ansatz，提出了一种扩展的Riccati方程有理展开方法，以构造非线性演化方程的多个精确解，并在计算机代数系统中实现。通过将该方法应用于Konopelchenko-Dubrovsky方程，验证了该方法的有效性和可靠性。该方法可以应用于数学物理学中的其他非线性演化方程。（c）2006年由Elsevier Inc.发布。

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《Applied mathematics and computation》 |2007年第2期|共16页
作者
Song L; Zhang HQ;
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正文语种 eng
中图分类应用数学;
关键词
symbolic computation; extended Riccati equation rational expansion method; exact solutions; nonlinear evolution equations; Konopelchenko-Dubrovsky equation; NONLINEAR EVOLUTION-EQUATIONS; AUTO-BACKLUND TRANSFORMATION; TRAVELING-WAVE SOLUTIONS; BURGERS-TYPE EQUATIONS; EXPLICIT EXACT-SOLUTIONS; BROER-KAUP EQUATIONS; TANH-FUNCTION METHOD; COMPOUND KDV-TYPE; ORDER; TERMS;

机译：符号计算;扩展的Riccati方程有理展开法;精确解;非线性演化方程;Konopelchenko-Dubrovsky方程;非线性演化方程;自动背景变换;行波解;伯格斯型方程;精确方程;BROER-UP方程;tanh函数法;复合KDV型;阶数;术语;

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专利

1. New exact solutions for the Konopelchenko-Dubrovsky equation using an extended Riccati equation rational expansion method and symbolic computation [J] . Song L, Zhang HQ Applied mathematics and computation . 2007,第2期

机译：使用扩展的Riccati方程有理展开方法和符号计算的Konopelchenko-Dubrovsky方程的新精确解
2. New Exact Solutions for Konopelchenko-Dubrovsky Equation Using an Extended Riccati Equation Rational Expansion Method [J] . SONG Li-Na, ZHANG Hong-Qing 理论物理通讯（英文版） . 2006,第005期

机译：使用扩展的Riccati方程有理展开方法的Konopelchenko-Dubrovsky方程的新精确解
3. A new generalized compound Riccati equations rational expansion method to construct many new exact complexiton solutions of nonlinear evolution equations with symbolic computation [J] . Wenting Li, Hongqing Zhang Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2009,第5期

机译：一种新的广义复合Riccati方程有理展开方法，用符号计算构造非线性发展方程的许多新的精确复解
4. Exact solutions for coupled mKdV equations by a new symbolic computation method [C] . L. I. Bangqing, M. A. Yulan International Conference on Information Technology for Manufacturing Systems . 2010

机译：通过新的符号计算方法耦合MKDV方程的精确解决方案
5. Finding closed-form solutions of difference equations by symbolic methods. [D] . Petkovsek, Marko. 1991

机译：用符号法寻找差分方程的闭式解。
6. Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G′/G)-expansion method [O] . Md Nur Alam, M Ali Akbar -1

机译：新的广义（G/ G）-展开法求解KP-BBM方程的精确行波解
7. Application of the improved F-expansion method with Riccati equation to find the exact solution of the nonlinear evolution equations [O] . Islam Md. Shafiqul, Khan Kamruzzaman, Akbar M. Ali 2017

机译：应用改进的F展开方法和Riccati方程找到非线性发展方程的精确解

New exact solutions for the Konopelchenko-Dubrovsky equation using an extended Riccati equation rational expansion method and symbolic computation

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