Periodic waves of a discrete higher order nonlinear Schrödinger equation

@article{Conte2006PeriodicWO,
  title={Periodic waves of a discrete higher order nonlinear Schr{\"o}dinger equation},
  author={R. Conte and Kwok Wing Chow},
  journal={Communications in Theoretical Physics},
  year={2006},
  volume={46},
  pages={961-965}
}
  • R. Conte, K. Chow
  • Published 5 April 2006
  • Mathematics
  • Communications in Theoretical Physics
The Hirota equation is a higher order extension of the nonlinear Schrodinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known result of the integrable Ablowitz–Ladik system. 
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TLDR
It is shown that intrinsic localized modes in a nonlinear lattice with a hard quartic nonlinearity are governed by the discrete Hirota equation and that a single-soliton solution exists only at definite values of the amplitude and velocity.
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