4.5 Article

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

Journal

NONLINEARITY
Volume 29, Issue 3, Pages 1036-1046

Publisher

IOP PUBLISHING LTD
DOI: 10.1088/0951-7715/29/3/1036

Keywords

coupling problem; long-time asymptotics; Camassa-Holm equation

Funding

  1. Austrian Science Fund (FWF) [Y330]
  2. AXA Research Fund under the Mittag-Leffler Fellowship Project
  3. Austrian Science Fund (FWF) [Y330] Funding Source: Austrian Science Fund (FWF)

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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.

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