Exponential asymptotics and Stokes lines in a partial differential equation

DOI10.1098/rspa.2005.1475zbMath1206.34076OpenAlexW2113296719WikidataQ115269223 ScholiaQ115269223MaRDI QIDQ5427629

David B. Mortimer, S. Jonathan Chapman

Publication date: 21 November 2007

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://ora.ox.ac.uk/objects/uuid:fead6bdb-d66a-4c9b-b773-48568d79f78c

zbMATH Keywords

Stokes linesexponential asymptoticsoptimal truncationBorel planeStokes smoothing

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items

Exponential asymptotics for elastic and elastic-gravity waves on flow past submerged obstacles ⋮ Free surface flow past topography: A beyond-all-orders approach ⋮ Unsteady flow over a submerged source with low Froude number ⋮ On the asymptotic behavior of a second‐order general differential equation ⋮ On the structure of parasitic gravity-capillary standing waves in the small surface tension limit ⋮ Recurrence relationship of successive level singulants ⋮ On reduced models for gravity waves generated by moving bodies ⋮ Late-order terms of second order ODEs in terms of pre-factors ⋮ New gravity–capillary waves at low speeds. Part 1. Linear geometries ⋮ New gravity–capillary waves at low speeds. Part 2. Nonlinear geometries ⋮ Three-dimensional capillary waves due to a submerged source with small surface tension ⋮ First-order general differential equation for multi-level asymptotics at higher levels and recurrence relationship of singulants ⋮ A note on the Stokes phenomenon in flow under an elastic sheet ⋮ Nonlinear q-Stokes phenomena for q-Painlevé I ⋮ The wake of a two-dimensional ship in the low-speed limit: results for multi-cornered hulls ⋮ Nanoptera in higher-order nonlinear Schrödinger equations: effects of discretization ⋮ Steady gravity waves due to a submerged source

Cites Work

• A singular perturbation problem in needle crystals
• On the higher–order Stokes phenomenon
• Asymptotics beyond All Orders in a Model of Crystal Growth
• New Stokes’ line in WKB theory
• Exponential asymptotics and Stokes lines in nonlinear ordinary differential equations
• Stokes Phenomenon and Matched Asymptotic Expansions
• Unnamed Item
• Unnamed Item