Article

**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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