广州大学学报：自然科学版
廣州大學學報：自然科學版
엄주대학학보：자연과학판
Journal og Guangzhou University:Natural Science Edition
2012年
1期
1-9
,共9页
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
非線性偏微分方程%擴展雙麯函數法%反應一擴散方程%精確解%符號計算
비선성편미분방정%확전쌍곡함수법%반응일확산방정%정학해%부호계산
nonlinear partial differential equation the extended hyperbolic function method reaction-diffusionequation exact solutions symbolic computation
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．
藉助于作者最近開髮的求解非線性偏微分方程精確解的符號計算軟件包——PDEsolver，穫得瞭一類非線性反應一擴散方程豐富的顯式精確解．WAZWAZ穫得的所有解為本文一些解的特例．另外還穫得瞭許多其他新的顯式精確解．結果錶明，擴展雙麯函數方法是WAZWAZ所提擴展雙麯正切方法的改進和推廣．擴展雙麯函數方法提供瞭精確求解非線性偏微分方程的有效方法．
차조우작자최근개발적구해비선성편미분방정정학해적부호계산연건포——PDEsolver，획득료일류비선성반응일확산방정봉부적현식정학해．WAZWAZ획득적소유해위본문일사해적특례．령외환획득료허다기타신적현식정학해．결과표명，확전쌍곡함수방법시WAZWAZ소제확전쌍곡정절방법적개진화추엄．확전쌍곡함수방법제공료정학구해비선성편미분방정적유효방법．
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.
