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Collapse of a Volterra soliton into a weak monotone shock wave

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  • Fernandez, J.-C.
  • Reinisch, G.

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).

Suggested Citation

  • Fernandez, J.-C. & Reinisch, G., 1978. "Collapse of a Volterra soliton into a weak monotone shock wave," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 91(3), pages 393-410.
    • Handle: RePEc:eee:phsmap:v:91:y:1978:i:3:p:393-410
    DOI: 10.1016/0378-4371(78)90186-3
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    1. Dominique Labbé & Arturo Montes, 1977. "L'Inflation Au Chili Et Les Problèmes De La Croissance Économique," Post-Print halshs-01730036, HAL.
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