Contribution of Higher Order Terms in the Reductive Perturbation Theory, II. A Case of Strongly Dispersive Wave

Contribution of higher order terms in the reductive perturbation theory has been investigated for nonlinear propagation of strongly dispersive ion plasma wave. The basic set of fluid equation is reduced to a coupled set of the nonlinear Schrödinger equation for the first order perturbed potential and a linear inhomogeneous equation for the second order perturbed potential. A steady state solution of the coupled set of equations has been solved analytically for the case of nonlinear amplitude modulation of the ion acoustic wave, which is nothing but the small wave number limit of the strongly dispersive ion plasma wave.