BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Generalized Solitary Waves In Karpman Equations: Effects Of Discre tization - Aaron Moston-duggan (Macquarie University) DTSTART:20221103T145000Z DTEND:20221103T152000Z UID:TALK185234@talks.cam.ac.uk DESCRIPTION:We consider generalizations of nonlinear Schrö\;dinger equ ations\, which we call &ldquo\;Karpman equations\,&rdquo\; that include ad ditional linear higher-order derivatives. Singularly perturbed Karpman equ ations produce generalized solitary waves (GSWs) in the form of solitary w aves with exponentially small oscillatory tails. Previous research on cont inuous Karpman equations has shown that GSWs occur in specific settings. W e use exponential asymptotic techniques to identify GSWs in singularly-per turbed continuous Karpman equations. We then study the effect of discretiz ation on GSWs by applying a finite-difference discretization to continuous Karpman equations. By comparing GSWs in these discrete Karpman equations with GSWs in their continuous counterparts\, we show that the oscillation amplitudes and periods in the GSWs differ in the continuous and discrete e quations. We also show that the parameter values at which there is a bifur cation between GSW solutions and solitary wave solutions depends on the ch oice of discretization. Finally\, by comparing different higher-order disc retizations of the fourth-order Karpman equation\, we show that the bifurc ation value tends to a nonzero constant for large orders\, rather than to 0 as in the associated continuous Karpman equation.\nCo-Authors: Mason Por ter and Christopher Lustri\n \; LOCATION:Seminar Room 1\, Newton Institute END:VEVENT END:VCALENDAR