一类(1+1)维演化方程的不变集和精确解

Invariant sets and exact solutions to the(1+1) dimensional evolution equations

讨论一类(1+1)维演化方程的不变集,并运用不变集求出此类方程的精确解。主要过程为:引入集合E0={u:ux=gxF(u)},求出一般的(1+1)维演化方程在此类集合中的不变解与相应的系数条件,进而在gx取特殊值时,得到此类方程所对应的精确解。

Invariant sets of the（1＋1） dimensional evolution equations are studied,which is utilized to derive exact solutions of those equations.The invariant set E0={u：ux=gxFu} is first introduced,and then it is shown that the equations admit the invariant set in E0 for certain coefficient functions.The exact solutions associated to the set E0 are obtained when gx is taken as several special values.