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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References

SHOWING 1-10 OF 28 REFERENCES
New-Type of Soliton Solutions for a Higher-Order Nonlinear Schrödinger Equation
It is shown that a higher-order nonlinear Schrodinger equation which describes propagation of pulses in optical fiber is solvable by means of the inverse scattering transform. The soliton solution
Product and Rational Decompositions of Theta Functions Representations for Nonlinear Periodic Waves
A class of periodic solutions of nonlinear evolution equations is expressed as products and rational expressions of theta/elliptic functions. Examples of equations treated include a coupled system of
Intrinsic localized modes as solitons of the discrete Hirota equation.
  • Konotop, Takeno
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
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.
Painlevé Analysis of a Higher-Order Nonlinear Schrödinger Equation
The Painleve test for integrability is applied to the Kodama-Hasegawa higher-order nonlinear Schrodinger equation which describes ultra-short light pulses in optical fibers. Only the four known
Nonlinear differential−difference equations
A method is presented which enables one to obtain and solve certain classes of nonlinear differential−difference equations. The introduction of a new discrete eigenvalue problem allows the exact
The Inverse scattering transform fourier analysis for nonlinear problems
A systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering. The form of each evolution
Soliton Solutions for Discrete Hirota Equation. II
For the minus sign discrete Hirota equation, we present a dark 1-soliton solution, a dark 2-soliton solution and its particular state, and a dark N -soliton solution. For the plus sign equation, we
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