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 ...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 stratified fluid 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 when the stratification is changed from exponential to linear. Finally the interaction of solitary waves is considered, and the Korteweg-de Vries equation and the Boussinesq equation are derived. Thus the known solutions of these equations can be rehed upon to provide the answers to the interaction problem.展开更多
文摘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 stratified fluid 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 when the stratification is changed from exponential to linear. Finally the interaction of solitary waves is considered, and the Korteweg-de Vries equation and the Boussinesq equation are derived. Thus the known solutions of these equations can be rehed upon to provide the answers to the interaction problem.
