Nanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular Chains

DOI10.1137/21M1398410zbMath1484.34061arXiv2102.07322OpenAlexW3214944642MaRDI QIDQ5016790

Christopher J. Lustri, Mason A. Porter, Guo Deng

Publication date: 14 December 2021

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.07322

zbMATH Keywords

solitary wavesexponential asymptoticsgranular chainnanoptera

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Singular perturbations for ordinary differential equations (34E15) Ordinary lattice differential equations (34A33) Soliton solutions (35C08)

Related Items

Solitary waves in FPU-type lattices ⋮ Exponential asymptotics of woodpile chain nanoptera using numerical analytic continuation ⋮ Nanoptera in nonlinear woodpile chains with zero precompression ⋮ Nanoptera in higher-order nonlinear Schrödinger equations: effects of discretization

Cites Work

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• Weakly non-local solitons for capillary-gravity waves: Fifth-degree Korteweg-de Vries equation
• Wave propagation in single column woodpile phononic crystals: Formation of tunable band gaps
• Existence of perturbed solitary wave solutions to a model equation for water waves
• Stokes' phenomenon; smoothing a Victorian discontinuity
• Highly nonlinear solitary waves in heterogeneous periodic granular media
• The devil's invention: Asymptotic, superasymptotic and hyperasymptotic series
• Existence theorem for solitary waves on lattices
• The generation of radiating waves in a singularly-perturbed Korteweg-de Vries equation
• Travelling waves in a chain of coupled nonlinear oscillators
• Nanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratio
• Nanoptera and Stokes curves in the 2-periodic Fermi-Pasta-Ulam-Tsingou equation
• Pulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gap
• Metastability of solitary waves in diatomic FPUT lattices
• Breathers in a locally resonant granular chain with precompression
• Nonlinear resonances leading to strong pulse attenuation in granular dimer chains
• Strongly nonlinear waves in locally resonant granular chains
• Solitary waves on FPU lattices: II. Linear implies nonlinear stability
• Nanoptera in a Period-2 Toda Chain
• Nonlinear elasticity and pressure-dependent wave speeds in granular media
• The equilibrium phase in heterogeneous Hertzian chains
• Interactions of solitary waves in integrable and nonintegrable lattices
• A numerical calculation of a weakly non-local solitary wave: the ϕ⁴breather
• Exponential asymptotics and Stokes lines in nonlinear ordinary differential equations
• Weakly Nonlocal Solitary Waves in a Singularly Perturbed Korteweg–De Vries Equation
• Quasiperiodic granular chains and Hofstadter butterflies
• Hyperasymptotics
• The fragmentation of a line of balls by an impact
• Uniform asymptotic smoothing of Stokes’s discontinuities
• Stokes Phenomenon and Matched Asymptotic Expansions
• Nanopteron-stegoton traveling waves in spring dimer Fermi-Pasta-Ulam-Tsingou lattices
• Standing lattice solitons in the discrete NLS equation with saturation
• Traveling waves and their tails in locally resonant granular systems
• Hyperasymptotics and the Linear Boundary Layer Problem: Why Asymptotic Series Diverge
• Self similar solutions to adhesive contact problems with incremental loading
• Impulse propagation in dissipative and disordered chains with power-law repulsive potentials