一类非线性发展方程的精确孤波解  

EXPLICIT EXACT SOLITARY WAVE SOLUTIONS TO A CLASS OF NONLINEAR EVOLUTION EQUATIONS

作　　者：张卫国[1] 

机构地区：[1]长沙铁道学院数力系

出　　处：《高校应用数学学报（A辑）》1996年第4期399-408,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

摘　　要：本文首先求出了非线性常微分方程ｕ″（ξ）＋ｍｕ２（ξ）＋ｎｕ３（ξ）＋ｐｕ（ξ）＝ｃ（Ⅰ）和ｕ″（ξ）＋ｒｕ′（ξ）＋ｍｕ２（ξ）＋ｎｕ３（ξ）＋ｐｕ（ξ）＝ｃ（Ⅱ）的显式精确解．进而求出了组合ＢＢＭ方程、Ｂｕｒｇｅｒｓ方程与组合ＢＢＭ方程混合型的钟状孤波解和扭状孤波解，同时还求出了广义Ｂｏｕｓｓｉｎｅｓｑ方程和广义ＫＰ方程的钟状和扭状孤波解．文中指出了其行波解可化为（Ⅰ）的发展方程既有钟状又有扭状孤波解，而其行波解可化为（Ⅱ）的发展方程没有钟状孤波解．In this paper, first we establish explicit exact solutions of the nonlinear ordinary differential equations u″(ξ)+mu 2(ξ)+nu 3(ξ)+pu(ξ)=c(Ⅰ) and u″(ξ)+ru′(ξ)+mu 2(ξ)+nu 3(ξ)+pu(ξ)=c(Ⅱ) . Secondly, we obtain bell profile and kink profile solitary wave solutions to the generalized BBM equation u t+auu x+bu 2u x+ru xx -u xxt =0 , and generalized Boussinesq equation u tt -x(u x+2auu x+3bu 2u x+ru xx +u xxx )=0 , and generalized KP equation x(u t+auu x+bu 2u x+ru xx +u xxx )+3k 2u yy =0 . Finally, we point out that the evolution equations with traveling wave solutions satisfying equation (Ⅰ) not only have bell profile solitary wave solutions but also have kink profile ones, the evolution equations with traveling wave solutions satisfying equation (Ⅱ) have no bell profile solitary wave solutions.

关 键 词：非线性 发展方程 孤波解 精确解 

分 类 号：O175.29[理学—数学]