【摘要】 本文用直接方法和假设方法的一种结合求出了一类较广泛的非线性波动方程ｕｔｔ－ａ１ｕｘｘ＋ａ２ｕｔ＋ａ４ｕ２＋ａ５ｕ３＝０的一些显式精确行波解．几个有重要应用的非线性数学物理方程，如４方程，Ｋｌｅｉｎ－Ｇｏｒｄｏｎ方程，Ｓｉｎｅ－Ｇｏｒｄｏｎ方程，及Ｓｉｎｈ－Ｇｏｒｄｏｎ方程的近似，Ｌａｎｄａｕ－Ｇｉｎｚｂｕｒｇ－Ｈｉｇｇｓ方程，Ｄｕｆｆｉｎｇ方程，非线性电报方程等都可作为该方程的特殊情形得到相应的显式精确解，这里方法也可推广到ｎ＋１维空间情形。更多还原

【Abstract】 Some explicit and exact travelling wave solutions for a class nonlinear wave equations are obtained by a kind of combination of the direct method and the ansatze method. Several important nonlinear equations of mathematical physics such as equation, Klein-Gordon equation, the approximate equations of sine-Gordon equation and sinh-Gordon equation, Landau-Ginzburg-Higgs equation, Duffing equation, nonlinear telegr aph equation are the special cases of the nonlinear wave equation presented in this paper. This method in the paper can also be applied to n+1 dimensional space nonlinear evolution equations.更多还原