Solitonic structures in KdV-based higher-order systems

Wave propagation in microstructured materials is studied using a Korteweg-d e Vries (KdV)-type nonlinear evolution equation. Due to the microstructure. nonlinear effects are described by a quartic elastic potential and dispers ive effects - by both the third- and the fifth-order space derivatives. The problem is solved numerically under harmonic initial condition. For nondis persive materials, the quartic elastic potential, compared with that of the second-order (KdV) one, leads to the formation of two additional discontin uities in the harmonic initial wave profile. This together with the additio nal dispersive effect is the reason for emerging complicated solitonic stru ctures (train of solitons, train of negative solitons and multiple solitons ) depending on the values of dispersion parameters. Chaotic motion results if both the third- and the fifth-order dispersion parameters take the small possible values. (C) 2001 Elsevier Science B.V. All rights reserved.