A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations. (4th February 2016)

• Record Type: Journal Article
• Authors: Eckhardt, Jonathan; Teschl, Gerald
• Is Part Of: Nonlinearity. Volume 29:Number 3(2016:Mar.)
• Page Start: 1036
• Page End: 1046
• Publication Date: 2016-02-04
• Subjects: coupling problem -- long-time asymptotics -- Camassa–Holm equation; Primary 37K40, 35Q35 -- Secondary 30D20, 37K20; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/29/3/1036
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We propose a novel technique for analysing the long-time asymptotics of integrable wave equations in the case when the underlying isospectral problem has a purely discrete spectrum. To this end, we introduce a natural coupling problem for entire functions, which serves as a replacement for the usual Riemann–Hilbert problem, which does not apply in these cases. As a prototypical example, we investigate the long-time asymptotics of the dispersionless Camassa–Holm equation.