| 一类非线性波动方程的显式精确解 |
| |
| 引用本文： | 尚亚东.一类非线性波动方程的显式精确解[J].应用数学学报,2000,23(1):21-30. |
| |
| 作者姓名： | 尚亚东 |
| |
| 作者单位： | 西安石油学院基础部,西安,710065 |
| |
| 摘 要： | 本文用直接方法和假设的一种结合求出了一类较广泛的非线性波动方程ｕｔｔ－ａ１ｕｘｘ＋ａ２ｕｔ＋ａ３ｕ＋ａ４ｕＳ＾２＋ａ５ｕ＾３＝０的一些显式精确行波解，贱个有重要的非线性数学物理方程，如φ＾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
|
| 关 键 词： | 非线性波动方程 精确解 行波解 显式精确解 |
EXPLICIT AND EXACT SOLUTIONS FOR A CLASS OF NONLINEAR WAVE EQUATIONS |
| |
| SHANG YADONG.EXPLICIT AND EXACT SOLUTIONS FOR A CLASS OF NONLINEAR WAVE EQUATIONS[J].Acta Mathematicae Applicatae Sinica,2000,23(1):21-30. |
| |
| Authors: | SHANG YADONG |
| |
| 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. |
| |
| Keywords: | Nonlinear wave equations direct method ansatze method exact solutions travelling wave solutions solitary wave solutions |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
