In the small dispersion regime, the KdV solution exhibits rapid oscillations in its spatio-temporal dependence. We show that these oscillations are caused by the presence of complex singularities that approach the real axis. We give a numerical estimate of the asymptotic dynamics of the poles.
Gargano, F., Ponetti, G., Sammartino, M., Sciacca, V. (2016). Complex singularities in KdV solutions. RICERCHE DI MATEMATICA, 65(2), 479-490 [10.1007/s11587-016-0269-9].
Complex singularities in KdV solutions
GARGANO, Francesco;SAMMARTINO, Marco Maria Luigi;SCIACCA, Vincenzo
2016-01-01
Abstract
In the small dispersion regime, the KdV solution exhibits rapid oscillations in its spatio-temporal dependence. We show that these oscillations are caused by the presence of complex singularities that approach the real axis. We give a numerical estimate of the asymptotic dynamics of the poles.
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