Nonlinear Waves Seminar: Ali Demirci

Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations

Ali Demirci

Department of Mathematics, Istanbul Technical University

Date and time: 

Thursday, August 27, 2015 - 4:00pm

Abstract: 

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 ansatz  reduces the study of DSWs in  (2+1) dimensions to finding DSW solutions of  (1+1) dimensional equations. With this ansatz the KP and 2DBO equations is exactly reduced to  cylindrical Korteweg-de Vries (cKdV) and  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.  It is concluded that the (2+1) DSW behavior along parabolic fronts can be effectively described  by the DSW  solutions of cylindrical (1+1) dimensional equations.