Higher order approximations in reductive perturbation method: strongly dispersive waves

Contribution of higher order terms in the perturbation expansion for the strongly dispersive ion-plasma waves is examined through the use of modified reductive perturbation method developed early by us. It is shown that the lowest order term in the expansion is governed by the nonlinear Schrödinger equation while the second-order term is governed by the linear Schrödinger equation. For the small wave number region a set of solution is presented for the evolution equations.