| 一类非线性反应一扩散方程丰富的显式精确解 |
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| 引用本文： | 黄勇,尚亚东.一类非线性反应一扩散方程丰富的显式精确解[J].广州大学学报(综合版),2012(1):1-9. |
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| 作者姓名： | 黄勇 尚亚东 |
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| 作者单位： | [1]计算机科学与教育软件学院广州大学 [2]数学与信息科学学院,广东广州510006 |
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| 基金项目： | 国家自然科学基金项目（10771041,40890150,40890153,60971093）;广东省科技计划项目（200813080701042）;广州市科普项目（2010KP035）资助 |
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| 摘 要： | 借助于作者最近开发的求解非线性偏微分方程精确解的符号计算软件包——PDEsolver，获得了一类非线性反应一扩散方程丰富的显式精确解．WAZWAZ获得的所有解为本文一些解的特例．另外还获得了许多其他新的显式精确解．结果表明，扩展双曲函数方法是WAZWAZ所提扩展双曲正切方法的改进和推广．扩展双曲函数方法提供了精确求解非线性偏微分方程的有效方法．
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| 关 键 词： | 非线性偏微分方程 扩展双曲函数法 反应一扩散方程 精确解 符号计算 |
Abundant explicit and exact solutions for a class of nonlinear reaction-diffusion equations |
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| HUANG Yong,SHANG Ya-dong.Abundant explicit and exact solutions for a class of nonlinear reaction-diffusion equations[J].Journal of Guangzhou University,2012(1):1-9. |
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| Authors: | HUANG Yong SHANG Ya-dong |
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| Institution: | ( School of Computer Science and Educational Software ; School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006 ,China) |
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| Abstract: | With the aid of a computer symbolic software package ＂PDESolver＂, developed by the authors re- cently to solve nonlinear partial differential equations exactly, abundant new exact and explicit solutions of a class of nonlinear reaction-diffusion equation are obtained. All solutions obtained by WAZWAZ are obtained a- gain as special case of some solutions in this paper. Many new explicit and exact solutions are also presented. The results indicated that the extended hyperbolic function method is an extension and improvement to the ex- tended tanh method presented by WAZWAZ. The extended hyperbolic function method provides an effective way to solve nonlinear partial differential equations exactly. |
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| Keywords: | nonlinear partial differential equation the extended hyperbolic function method reaction-diffusionequation exact solutions symbolic computation |
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