Higher Order Approximation in the Reductive Perturbation Method. II. The Strongly Dispersive System

抄録

For the strongly dispersive nonlinear system, the higher-order effects in the reductive perturbation method proposed by Taniuti et al. are investigated. It is shown that the secular terms appearing in the higher-order terms are eliminated by adding to the nonlinear Schrödinger equation the functional derivatives of the higher-order conserved quantities, the physical effects of which are given by the renormalization of the frequencies and the velocities of the envelope solitons.