【摘要】 <正> §1.引言自从N.J.Zabusky和M.D.Kruskal通过数值计算发现孤立子以后,孤立波的相互作用问题引起了人们广泛的注意.不少作者对浅水中的孤立波相互作用作了研究,例如,苏兆星和Mine先后采用摄动法和数值方法处理了单层流体中孤立波的迎撞问题,最近,邹启苏和苏兆星又用多重尺度法和有限差分法分析了孤立波的追撞相互作用,并得出结论:在二阶近似下,两孤立波在追撞相互作用后各自保持波形不变,而且不产生尾波列.为了研究分层流体中内孤立波的相互作用,戴世强建立了具有三阶精度的二维不可更多还原

【Abstract】 This paper deals with the over taking collisions between solitary waves ofsame mode in a stratified fluid by using the reductive perturbation methodcombined with the multiple-scale method and the two-soliton solution of theKdV equation. The numerical solution to the resulting second-order perturbationequation leads to the approximate wave profile of the fast-mode solitary wavesduring the collisions. The results show that after the interaction, the two pairsof solitary waves preserve their profiles without the generation of secondarywave trains to the second-order approximation, which is in agreement with theprevious conclusion for the case of single-layer fluid. In addition, it is found thatin contrast to the situations of weak interaction, e. g., the head-on collisions orthe overtaking collisions of solitary waves of different modes, in the case studiedherein, a kind of "amplitude transfer" may occur during the collisions and themaximum amplitude of the merged wave will be smaller than that of impingingsolitary waves.更多还原