SOLITARY WAVES IN STRATIFIED FLUIDS AND THEIR INTERACTION

A systematic procedure is proposed for obtaining solutions for soli-tary waves in stratified fluids. The stratification of the fluid is assumed to be expo-nential or linear. Its comparison with existing results for an exponentially stratifiedfluid shows agreement, and it is found that for the odd series of solutions the direc-tion of displacement of the streamlines from their asymptotic levels is reversed whenthe stratification is changed from exponential to linear. Finally the interaction ofsolitary waves is considered, and the Korteweg-de Vries equation and the Boussinesqequation are derived. Thus the known solutions of these equations can be rehed uponto provide the answers to the interaction problem.