Affiliation:
1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. O. Box 253, P. R. China
Abstract
In this paper, we construct the generalized perturbation ([Formula: see text], [Formula: see text])-fold Darboux transformation of the fifth-order modified Korteweg-de Vries (KdV) equation by the Taylor expansion. We use this transformation to derive the higher-order rational soliton solutions of the fifth-order modified KdV equation. We find that these higher-order rational solitons admit abundant interaction structures. We graphically present the dynamics behaviors from the first- to fourth-order rational solitons. Furthermore, by the Miura transformation, we obtain the complex rational soliton solutions of the fifth-order KdV equation.
Funder
Natural Science Foundation of Shanghai
Publisher
World Scientific Pub Co Pte Lt
Subject
Condensed Matter Physics,Statistical and Nonlinear Physics