Convergent analytic solutions for homoclinic orbits in reversible and non-reversible systems

DOI10.1007/s11071-013-0902-zzbMath1281.34079arXiv1211.4354OpenAlexW3099515852MaRDI QIDQ2436918

Gaetana Gambino, S. Roy Choudhury

Publication date: 27 February 2014

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.4354

zbMATH Keywords

homoclinic orbitstraveling wave solutionreversible and non-reversible systemsShil'nikov analysis

Mathematics Subject Classification ID

Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Traveling wave solutions (35C07)

Related Items (3)

On the existence of heteroclinic cycles in some class of 3-dimensional piecewise affine systems with two switching planes ⋮ Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: phase-plane, multi-infinite series and variational approaches ⋮ Smooth and non-smooth traveling wave solutions of some generalized Camassa-Holm equations

Cites Work

• Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems
• Detecting stable-unstable nonlinear invariant manifold and homoclinic orbits in mechanical systems
• Si'lnikov chaos and Hopf bifurcation analysis of Rucklidge system
• Perturbed homoclinic solutions in reversible 1:1 resonance vector fields
• Weakly non-local solitons for capillary-gravity waves: Fifth-degree Korteweg-de Vries equation
• Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
• Cascades of reversible homoclinic orbits to a saddle-focus equilibrium
• A simple global characterization for normal forms of singular vector fields
• Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations
• A multiplicity result for solitary gravity-capillary waves in deep water via critical-point theory
• Orbits homoclinic to exponentially small periodic orbits for a class of reversible systems. Application to water waves
• Analytic approximation of the homoclinic orbits of the Lorenz system at \(\sigma=10\), \(b=8/3\) and \(\rho=13. 926\dots\)
• Sources, sinks and wavenumber selection in coupled CGL equations and experimental implications for counter-propagating wave systems
• Stable bound states of pulses in an excitable medium
• Analysis of a 3D chaotic system
• Complex Dynamical Behaviors of the Chaotic Chen's System
• Snaking of Multiple Homoclinic Orbits in Reversible Systems
• Nonlinearly Resonant Surface Waves and Homoclinic Bifurcation
• Stability, Instability and Chaos
• A global investigation of solitary-wave solutions to a two-parameter model for water waves
• Moving embedded solitons
• CHEN'S ATTRACTOR EXISTS
• Homoclinic orbits to small periodic orbits for a class of reversible systems
• Dynamics of Embedded Solitons in the Extended Korteweg–de Vries Equations
• EXACT HOMOCLINIC ORBITS AND HETEROCLINIC FAMILIES FOR A THIRD-ORDER SYSTEM IN THE CHAZY CLASS XI (N = 3)
• Numerical continuation of homoclinic orbits to non-hyperbolic equilibria in planar systems
• Elements of applied bifurcation theory
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