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