Collapse of a Volterra soliton into a weak monotone shock wave

✍ Scribed by J.-C. Fernandez; G. Reinisch

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 689 KB
• Volume: 91
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(78)90186-3

✦ Synopsis

The perturbation of the stationary solitary solution of a feeder-eater Volterra equation by a small linear dissipative-like term is studied both numerically and analytically and leads to the existence of "quasi-solitons" which are hybrid non-stationary profiles constituted each by a high amplitude, exponentially damped soliton followed by a small amplitude uniform residue left behind the advancing pulse and shown to be a stationary Burgers shock wave. These quasi° solitons appear as stable as unperturbed solitons and preserve their own identity despite nonlinear interactions. They seem to be a consequence of the finiteness of the initial condition norm (measured above the reference noise level).