English

Beyond Nonlinear Schr\"odinger Equation Approximation for an Anharmonic Chain with Harmonic Long Range Interaction

solv-int 2007-05-23 v1 Exactly Solvable and Integrable Systems

Abstract

Multi scales method is used to analyze a nonlinear differential-difference equation. In order ϵ3\epsilon^3 the NLS equation is found to determine the space-time evolution of the leading amplitude. In the next order this has to satisfy a complex mKdV equation (the next in the NLS hierarchy) in order to eliminate secular terms. The zero dispersion point case is also analyzed and the relevant equation is a modified NLS equation with a third order derivative term included

Keywords

Cite

@article{arxiv.solv-int/9910006,
  title  = {Beyond Nonlinear Schr\"odinger Equation Approximation for an Anharmonic Chain with Harmonic Long Range Interaction},
  author = {D. Grecu and Anca Visinescu and A. S. Carstea},
  journal= {arXiv preprint arXiv:solv-int/9910006},
  year   = {2007}
}

Comments

6 pages, LaTeX, paper presented at NEEDS'99 Kolymbari, Crete

R2 v1 2026-07-22T20:09:17.160Z