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We propose a novel technique for analyzing the long-time asymptotics ofintegrable wave equations in the case when the underlying isospectral problemhas purely discrete spectrum. To this end, we introduce a natural couplingproblem for entire functions, which serves as a replacement for the usualRiemann-Hilbert problem, which does not apply in these cases. As a prototypicalexample, we investigate the long-time asymptotics of the dispersionlessCamassa-Holm equation.

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