MKdV方程、SG方程与非线性Schrǒdinger方程的关系

The Relation or MKdV and SG Equation with Nonlinear Schrdinger Equation

ＭＫｄＶ方程和ＳＧ方程是描述非线性波动具有代表性的两个重要方程。本文通过对这两个方程进行小振幅下的Ｆｏｕｒｉｅｒ展开分析和呼吸子解分析，得出在小振幅慢变位相情形下都满足非线性Ｓｃｈｒｄｉｎｇｅｒ方程，从而揭示了非线性波动方程的一些共同特性和内在联系．

The MKdV equation and SG equation are two typical important equations describing nonlinear wave phenomena. In the present paper.these two equations are discussed by means of Fourier analysis and decomposition of breather solution under the condition of small-amplitude. It is found that in the case of small-amplitude and slawly varying phase both equations can be related to nonlinear Schrdinger equation. Then some homogeneity and intrinsical relations of nonlinear wave equation are revealed.