Nonlinearity 29, 1036-1046 (2016) [DOI: 10.1088/0951-7715/29/3/1036]

A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations

Jonathan Eckhardt and Gerald Teschl

We propose a novel technique for analyzing the long-time asymptotics of integrable wave equations in the case when the underlying isospectral problem has 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.

MSC2010: Primary 37K40, 35Q35; Secondary 30D20, 37K20
Keywords: Coupling problem, long-time asymptotics, Camassa-Holm equation

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