Solitonic structures in KdV-based higher-order systems

✍ Scribed by A. Salupere; J. Engelbrecht; G.A. Maugin

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 449 KB
• Volume: 34
• Category: Article
• ISSN: 0165-2125
• DOI: 10.1016/s0165-2125(01)00069-5

✦ Synopsis

Wave propagation in microstructured materials is studied using a Korteweg-de Vries (KdV)-type nonlinear evolution equation. Due to the microstructure, nonlinear effects are described by a quartic elastic potential and dispersive effects -by both the third-and the fifth-order space derivatives. The problem is solved numerically under harmonic initial condition. For nondispersive materials, the quartic elastic potential, compared with that of the second-order (KdV) one, leads to the formation of two additional discontinuities in the harmonic initial wave profile. This together with the additional dispersive effect is the reason for emerging complicated solitonic structures (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.