Higher-order Internal Solitary Waves In Stratified Fluids

The research on the solitary waves in stratified fluids, involved in mechanics, physics, applied mathematics, practical engineering and etc., is an advanced field which is of powerful practical and theoretical significance. The finite amplitude solitary waves in stratified fluids of finite depth, in which the density varies with depth in lower layer but keeps uniform in upper layer, are investigated by using the method of combination of theoretical analysis and symbolic computation. The first, second and third-order evolution equation are derived by combining the PLK method and the matching of asymptotic expansions. The coefficients of equation for special density distribution—strong stratification are calculated. And the curves of the second and third-order equations are drawed. It is found that the first and second-order evolution equation are consistent with the known ones, second and third-order numerical solutions have significant improvement than first-order.