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arXiv · 1305.2487

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

Jonathan Eckhardt·Gerald Teschl
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Abstract

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.

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Jonathan Eckhardt, Gerald Teschl. 2016-02-04. A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations. https://doi.org/10.1088/0951-7715%2F29%2F3%2F1036

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