On the existence of homoclinic and heteroclinic orbits for differential equations with a small parameter

DOI10.1017/S0956792500000449zbMath0739.34041OpenAlexW2003467148MaRDI QIDQ3978073

J. G. B. Byatt-Smith

Publication date: 25 June 1992

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0956792500000449

zbMATH Keywords

heteroclinic orbitshomoclinic orbits

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (7)

The generation of radiating waves in a singularly-perturbed Korteweg-de Vries equation ⋮ On Short‐Scale Oscillatory Tails of Long‐Wave Disturbances ⋮ Weakly non-local solitary wave solutions of a singularly perturbed Boussinesq equation ⋮ Existence theory of capillary-gravity waves on water of finite depth ⋮ A note on the Stokes phenomenon in flow under an elastic sheet ⋮ Radiating solitary waves of a model evolution equation in fluids of finite depth ⋮ Analytical and numerical studies of a singularly perturbed Boussinesq equation.

Cites Work

• Travelling wave solutions of the Kuramoto-Sivashinsky equation
• A singular perturbation problem in needle crystals
• A theory of solitary water-waves in the presence of surface tension
• Accurate computations for steep solitary waves
• Long-wave instability at the interface between two viscous fluids: Thin layer effects
• A Differential Equation Connected with the Dendritic Growth of Crystals
• Existence and uniqueness of heteroclinic orbits for the equation λu‴ + u′ = f(u)

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