The use of Borel-summation in the establishment of non-existence of certain travelling-wave solutions of the Kuramoto-Sivashinsky equation

DOI10.1016/0165-2125(92)90055-7zbMath0785.34037OpenAlexW2056235632MaRDI QIDQ1205390

R. H. J. Grimshaw

Publication date: 1 April 1993

Published in: Wave Motion (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0165-2125(92)90055-7

zbMATH Keywords

Kuramoto-Sivashinsky equationnonexistence of regular shocks

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Asymptotic expansions of solutions to ordinary differential equations (34E05) Other special methods applied to PDEs (35A25)

Related Items

Asymptotics beyond all orders and analytic properties of inverse Laplace transforms of solutions ⋮ On traveling-wave solutions of the Kuramoto-Sivashinsky equation ⋮ Something hidden in the Fourier series and its partial sum: Solitary wave solutions to polynomial nonlinear differential equations ⋮ Exponential asymptotic expansions and approximations of the unstable and stable manifolds of singularly perturbed systems with the Hénon map as an example

Cites Work

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• Structural stability of the Korteweg-de Vries solitons under a singular perturbation
• The non-existence of a certain class of travelling wave solutions of the Kuramoto-Sivashinsky equation
• Asymptotics beyond All Orders in a Model of Crystal Growth