6533b7d1fe1ef96bd125c427

RESEARCH PRODUCT

Complex singularities in KdV solutions

G. PonettiVincenzo SciaccaMarco SammartinoFrancesco Gargano

subject

Complex singularities Padé approximation Borel and power series methods Dispersive shocksApplied MathematicsGeneral MathematicsNumerical analysis010102 general mathematicsMathematical analysis01 natural sciences010305 fluids & plasmasAsymptotic dynamics0103 physical sciencesPadé approximantGravitational singularity0101 mathematicsAlgebra over a fieldKorteweg–de Vries equationDispersion (water waves)Complex planeMathematics

description

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.

yearjournalcountryeditionlanguage
2016-04-01
10.1007/s11587-016-0269-9http://hdl.handle.net/10447/198380