Traveling solitons in long-range oscillator chains

@article{Miloshevich2016TravelingSI,
  title={Traveling solitons in long-range oscillator chains},
  author={George Miloshevich and Jean Pierre Nguenang and Thierry Dauxois and Ramaz Khomeriki and Stefano Ruffo},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2016},
  volume={50}
}
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 1<α⩽3. We obtain an analytic perturbative expression of traveling envelope solitons by introducing a non linear Schrödinger equation for the slowly varying amplitude of short wavelength modes. Due to the non analytic properties of the dispersion relation, it is crucial to… 

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List of Portraits Preface Part I. Different Classes of Solitons: Introduction 1. Nontopological solitons: the Korteweg-de Vries equation 2. Topological soltitons: sine-Gordon equation 3. Envelope
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