Non-persistence of homoclinic connections for perturbed integrable reversible systems

DOI10.1023/A:1021893602144zbMath0929.34025OpenAlexW1571668004MaRDI QIDQ1288143

Eric Lombardi

Publication date: 16 January 2000

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1021893602144

zbMATH Keywords

periodic orbitsdynamicspersistencehomoclinic connectionanalytic reversible vector fieldperturbed integrable reversible systemsreversible homoclinic connections

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Qualitative investigation and simulation of ordinary differential equation models (34C60) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity. I ⋮ Mass and spring dimer Fermi–Pasta–Ulam–Tsingou nanopterons with exponentially small, nonvanishing ripples ⋮ Embedded solitons: Solitary waves in resonance with the linear spectrum ⋮ A variational approach to the stability of an embedded NLS soliton at the edge of the continuum ⋮ Existence of generalized solitary wave solutions of the coupled KdV-CKdV system

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