SOLITARY WAVES AT THE INTERFACE OF A TWO-LAYER FLUID

In this paper,we discuss the solitary waves at the interface of a two-layer incompressible inviscid fluid confined by two horizontal rigidwalls,taking the effect of surface tension into account.First of all,we establish the basic equations suitable for the model considered,and hence derive the Korteweg-de Vries(KdV)equation satisfied bythe first-order elevation of the interface with the aid of the reduc-tive perturbation method under the approximation of weak dispersion.Itis found that the KdV solitary waves may be convex upward or downward.It depends on whether the signs of the coefficients α and μof the KdVequation are the same or not.Then we examine in detail two criticalcases,in which the nonlinear effect and the dispersion effect cannotbalance under the original approximation.Applying other appropriateapproximations,we obtain the modified KdV equation for the criticalcase of first kind(α=0),and conclude that solitary waves cannot existin the case considered as μ>0,but may still occur as μ<0,be