应用数学
應用數學
응용수학
MATHEMATICA APPLICATA
2011年
4期
699-704
,共6页
(1/G)-展开法%行波解%五阶KdV方程%齐次平衡
(1/G)-展開法%行波解%五階KdV方程%齊次平衡
(1/G)-전개법%행파해%오계KdV방정%제차평형
(1/G) -expansion method%Travelling wave solution%Fifth order KdV equation%Homogeneous balance
本篇论文首次提出(1/G) -展开法,用于求解非线性演化方程的行波解.将该法应用于五阶KdV方程的求解,当参数满足一定条件时,该方程可化为Sawada-Kotera (SK)方程、Caudrey-Dodd-Gibbon(CDG)方程、Kaup-Kupershmidt (KK)方程、Lax方程和Ito方程.其解可被表示为含两个任意参数的双曲函数解和三角函数解,作为示例,文中仅给出了SK方程和Ito方程的行波解.(1/G)-展开法具有直接、简捷与基本的特点,可以适用于数学物理中其它非线性演化方程的求解.
本篇論文首次提齣(1/G) -展開法,用于求解非線性縯化方程的行波解.將該法應用于五階KdV方程的求解,噹參數滿足一定條件時,該方程可化為Sawada-Kotera (SK)方程、Caudrey-Dodd-Gibbon(CDG)方程、Kaup-Kupershmidt (KK)方程、Lax方程和Ito方程.其解可被錶示為含兩箇任意參數的雙麯函數解和三角函數解,作為示例,文中僅給齣瞭SK方程和Ito方程的行波解.(1/G)-展開法具有直接、簡捷與基本的特點,可以適用于數學物理中其它非線性縯化方程的求解.
본편논문수차제출(1/G) -전개법,용우구해비선성연화방정적행파해.장해법응용우오계KdV방정적구해,당삼수만족일정조건시,해방정가화위Sawada-Kotera (SK)방정、Caudrey-Dodd-Gibbon(CDG)방정、Kaup-Kupershmidt (KK)방정、Lax방정화Ito방정.기해가피표시위함량개임의삼수적쌍곡함수해화삼각함수해,작위시례,문중부급출료SK방정화Ito방정적행파해.(1/G)-전개법구유직접、간첩여기본적특점,가이괄용우수학물리중기타비선성연화방정적구해.
The (1/G) -expansion method is proposed to find travelling wave solutions of the generalized fifth order KdV equation(fKdV) which can become the Sawada-Kotera (SK) equation,Caudrey-Dodd-Gibbon(CDG) equation,Kaup-Kupershmidt(KK) equation,Lax equation and Ito equation if the coefficients of the fKdV are taken as the different values,respectively.As a result,exact travelling wave solutions expressed by hyperbolic functions and trigonometric functions with two arbitrary constants of the fKdV are obtained provided its coefficients satisfy a constraint condition,based on which the travelling wave solutions of mentioned several special forms of the fKdV can also be derived,as illustrative examples,the travelling wave solutions of the SK equation and Ito equation are given here.The proposed method is direct,concise and elementary,and it can be used for other nonlinear evolution equations in mathematical physics.
