Approximation of small-amplitude weakly coupled oscillators by discrete nonlinear Schrödinger equations

DOI10.1142/S0129055X1650015XzbMath1347.37123arXiv1509.06389MaRDI QIDQ2822029

Dmitry E. Pelinovsky, Tiziano Penati, Simone Paleari

Publication date: 26 September 2016

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.06389

zbMATH Keywords

energy methodnormal formsdiscrete nonlinear Schrödinger equationsKlein-Gordon latticeexistence and stability of breatherssmall-amplitude approximations

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Lattice dynamics; integrable lattice equations (37K60) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Normal forms for nonlinear problems in mechanics (70K45)

Related Items (9)

Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein-Gordon equation and numerical comparisons ⋮ On the nonexistence of degenerate phase-shift discrete solitons in a dNLS nonlocal lattice ⋮ Coupled pendula chains under parametric \(\mathcal{PT}\)-symmetric driving force ⋮ On the nonexistence of degenerate phase-shift multibreathers in Klein-Gordon models with interactions beyond nearest neighbors ⋮ Reduction of a damped, driven Klein–Gordon equation into a discrete nonlinear Schrödinger equation: Justification and numerical comparison ⋮ Traveling and standing waves in coupled pendula and Newton's cradle ⋮ Long-time stability of small FPU solitary waves ⋮ Existence and Stability of Klein–Gordon Breathers in the Small-Amplitude Limit ⋮ Continuation of spatially localized periodic solutions in discrete NLS lattices via normal forms

Cites Work

• Long time stability of small-amplitude breathers in a mixed FPU-KG model
• Nonlinear Instabilities of Multi-Site Breathers in Klein-Gordon Lattices
• Soliton Interaction with Slowly Varying Potentials
• Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein–Gordon lattices
• Justification of the log--KdV Equation in Granular Chains: The Case of Precompression
• Breathers and Q-Breathers: Two Sides of the Same Coin
• From Newton's Cradle to the Discrete $p$-Schrödinger Equation
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