Homoclinic orbits for the perturbed sine-Gordon equation

DOI<283::AID-CPA1>3.0.CO;2-2 10.1002/(SICI)1097-0312(200003)53:3<283::AID-CPA1>3.0.CO;2-2zbMath1033.35107OpenAlexW2060849920MaRDI QIDQ4487955

Jalal Shatah, Chongchun Zeng

Publication date: 25 June 2000

Full work available at URL: https://doi.org/10.1002/(sici)1097-0312(200003)53:3<283::aid-cpa1>3.0.co;2-2

zbMATH Keywords

perturbationhomoclinic solutionsLyapunov-Schmidt methodMelnikov functionsine-Gordon equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems (37K99) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50)

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Analysis on global and chaotic dynamics of nonlinear wave equations for truss core sandwich plate ⋮ A BRIEF SURVEY ON CONSTRUCTING HOMOCLINIC STRUCTURES OF SOLITON EQUATIONS ⋮ Normally elliptic singular perturbations and persistence of homoclinic orbits ⋮ Homoclinic solutions for Davey-Stewartson equation ⋮ Chaos in the beam equation ⋮ Explicit homoclinic tube solutions and chaos for Zakharov system with periodic boundary ⋮ Homoclinic orbits for perturbed coupled nonlinear Schrödinger equations ⋮ Chaotic-like transfers of energy in Hamiltonian PDEs ⋮ Chaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems ⋮ Homoclinic orbits for coupled modified nonlinear Schrödinger equations ⋮ Persistence of Homoclinic Orbits under White Noise Perturbation ⋮ Strange Attractors for Periodically Forced Parabolic Equations ⋮ Novel homoclinic and heteroclinic solutions for the 2D complex cubic Ginzburg-Landau equation

Cites Work

• Geometry of the modulational instability. III: Homoclinic orbits for the periodic sine-Gordon equation
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Global bifurcations and chaos. Analytical methods
• A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
• Stable and Random Motions in Dynamical Systems
• The sine-gordon and sinh-gordon equations on the circle
• The rigidity of sine‐gordon breathers
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