Second-Order Theory Of Internal Solitary Waves In Stratified Fluids Of Finite Depth

The research on the solitary waves in stratified fluids, involved in mechanics,physics, applied mathematics, practical engineering and etc., is an advanced field whichis of powerful practical and theoretical significance. The solitary waves in stratifiedfluids of finite depth, in which the density varies with depth in lower layer but keepsuniform in upper layer, are investigated by using the method of combination oftheoretical analysis and symbolic computation. The first and second-order theories arederived respectively from the Long equation and the Euler equation by using the balancebetween the nonlinearity and the dispersion with the scaling μ = O(ε ), via the combinationof the PLK method and the matching of asymptotic expansions in virtue of the computeralgebraic software MATHEMATICA. It is found the evolution equation and its solutionderived for the first-order wave amplitude consist with the classical ones, and thesecond-order equation obtained by the two methods herein is of identity.