By choosing some appropriate exponential weight functions we prove that the essential spectra and the eigenvalues ( except the simple zero eigenvalue ) have negative real parts , thus we get the locally asymptotically exponential stability of travelling waves ( al ) and ( a2 ) in some weighted spaces 通過選用合適的權函數(shù),我們證得在加權空間線性化算子的本質譜和除簡單特征值零以外的特征值均具有負實部。因此,我們得到行波( a1 ) , ( a2 )在加權的l ~ 2 ( r )空間的局部漸近指數(shù)穩(wěn)定。