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
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.