Exact analytical solutions for the variational equations derived from the nonlinear Schrodinger equation

A. B. Moubissi, K. Nakkeeran, Abdosllam Moftah Abobaker

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5 Citations (Scopus)


By means of the variational formalism for the nonlinear Schrodinger equation, we find an explicit relation for the power of a pulse in terms of its duration, chirp and fiber parameters (group-velocity dispersion and self-phase modulation parameters). Then, using that relation, we derive the explicit analytical expressions for the variational equations corresponding to the amplitude, width, and chirp of the pulse. The derivation of the analytical expressions for the variational equations is possible for the condition when the Hamiltonian of the system is zero. Finally, for Gaussian and hyperbolic secant ansatz, we show good agreement between the results obtained from the analytical expressions and the direct numerical simulation of the nonlinear Schrodinger equation.

Original languageEnglish
Article number026603
Number of pages4
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number2
Publication statusPublished - 8 Aug 2007


  • fiber transmission-systems
  • analytical design
  • dispersion
  • radiation
  • solitons

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