Stokes-multiplier expansion in an inhomogeneous differential equation with a small parameter

E I Olafsdottir, A B O Daalhuis, J Vanneste

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

Accurate approximations to the solutions of a second-order inhomogeneous equation with a small parameter epsilon are derived using exponential asymptotics. The subdominant homogeneous solutions that are switched on by an inhomogeneous solution through a Stokes phenomenon are computed. The computation relies on a resurgence relation, and it provides the epsilon-dependent Stokes multiplier in the form of a power series. The epsilon-dependence of the Stokes multiplier is related to constants of integration that earl be chosen arbitrarily in the WKB-type construction of the homogeneous solution.

The equation under study governs the evolution of special solutions of the Boussinesq equations for rapidly rotating, strongly stratified fluids. In this context, the switching on of subdominant homogeneous solutions is interpreted as the generation of exponentially small inertia-gravity waves.

Original languageEnglish
Pages (from-to)2243-2256
Number of pages14
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume461
Issue number2059
DOIs
Publication statusPublished - 8 Jul 2005

Keywords / Materials (for Non-textual outputs)

  • exponential asymptotics
  • Stokes phenomenon
  • WKB expansion
  • inertia-gravity waves
  • RANK-ONE
  • HYPERASYMPTOTIC SOLUTIONS
  • SINGULARITY
  • BALANCE

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