CAJ | 학술논문

为研究一个非线性波方程,借助符号计算软件 Maple,采用李对称分析并结合动力系统理论的分支方法,得到该方程的李点对称和行波解的精确参数表达式,并给出了行波系统的相图。结果表明,李对称分析对于研究非线性发展方程是一个有效的数学工具。
위연구일개비선성파방정,차조부호계산연건 Maple,채용리대칭분석병결합동력계통이론적분지방법,득도해방정적리점대칭화행파해적정학삼수표체식,병급출료행파계통적상도。결과표명,리대칭분석대우연구비선성발전방정시일개유효적수학공구。
To study a nonlinear wave equation,the Lie symmetry analysis method and the bifurcation theory of dynamical system are used to obtain the symmetries of the equation and the exact parametric representations of traveling wave solutions with the aid of Maple,and the phase portraits of traveling wave system are given.The simulation results show that the Lie symmetry analysis is a effective mathematical tool for study nonlinear evolution equations.