Nonlinear Waves Seminar: Ali Demirci
Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations
Ali Demirci
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Date and time:Ìý
Thursday, August 27, 2015 - 4:00pm
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Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using parabolic front initial data. Employing a front tracking type ansatzÌý reduces the study of DSWs inÌý (2+1) dimensions to finding DSW solutions ofÌý (1+1) dimensional equations. With this ansatz the KP and 2DBO equations is exactly reduced toÌý cylindrical Korteweg-de Vries (cKdV) andÌý cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations and 2+1 systems are compared — with excellent agreement.Ìý It is concluded that the (2+1) DSW behavior along parabolic fronts can be effectively describedÌý by the DSWÌý solutions of cylindrical (1+1) dimensional equations.