Collapse of a Volterra soliton into a weak monotone shock wave

J.-C. Fernandez and G. Reinisch

Physica A: Statistical Mechanics and its Applications, 1978, vol. 91, issue 3, 393-410

Abstract: 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).

Date: 1978
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:91:y:1978:i:3:p:393-410

DOI: 10.1016/0378-4371(78)90186-3

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