The modified reductive perturbation method as applied to Boussinesq equation: strongly dispersive case

In this work, we extended the application of “the modified reductive perturbation method” to Boussinesq equation for strongly dispersive case and tried to obtain the contribution of higher order terms in the perturbation expansion. It is shown that the first order term in the perturbation expansion is governed by the non-linear Schrödinger equation and the second order term is governed by the linearized Schrödinger equation with a non-homogeneous term. In the long-wave limit, a travelling wave type of solution to these equations is also given.