【摘要】 用未知函数的变换将Sine Gordon方程变换成新未知函数及其偏导数为变元的多项式型的非线性偏微分方程。这个偏微分方程可用F展开法求解。因这里的F代表每一个Jacobi椭圆函数,所以F展开法可看作是Jacobi椭圆函数展开方法的概括惑浓缩,并不需要计算Jacobi椭圆函数,我们得到Sine Gordon方程的10种借Jacobi椭圆函数和双曲函数表示的精确解。更多还原

【Abstract】 By a transformation of dependent variable,the Sine-Gordon equation is converted into a nonlinear partial differential equation (NPDE) of a polynomial type of new dependent variable and its partial derivatives.The NPDE can be solved by F-expansion,which can be thought of as a generalization or concentration Jacobi elliptic functions.Without calculating Jacobi elliptic functions 10 kinds of exact solutions expressed by various Jacobi elliptic functions and hyperbolic functions of the Sine-Gordon equation are obtained.更多还原