Traveling Solitons in Long-Range Oscillator Chains
arXiv:1611.05350 · doi:10.1088/1751-8121/aa5fcf
Abstract
We investigate the existence and propagation of solitons in a long-range extension of the quartic Fermi-Pasta-Ulam (FPU) chain of anharmonic oscillators. The coupling in the linear term decays as a power-law with an exponent greater than 1 and less than 3. We obtain an analytic perturbative expression of traveling envelope solitons by introducing a Non Linear Schrodinger (NLS) equation for the slowly varying amplitude of short wavelength modes. Due to the non analytic properties of the dispersion relation, it is crucial to develop the theory using discrete difference operators. Those properties are also the ultimate reason why kink-solitons may exist but are unstable, at variance with the short-range FPU model. We successfully compare these approximate analytic results with numerical simulations.
10 pages, 4 figures
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Cited by in corpus (6)
- Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs
- Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
- Fermi-Pasta-Ulam chains with harmonic and anharmonic long-range interactions
- The effect of long-range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on-site potential
- Low-frequency discrete breathers in long-range systems without on-site potential
- Pulse solutions of the fractional effective models of the Fermi-Pasta-Ulam lattice with long-range interactions