Behavior of different ansätze in the generalized projection operator method

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Abstract

Using the recently reported generalized projection operator method for the nonlinear Schrödinger equation, we derive the generalized pulse parameters equations for ansätze like hyperbolic secant and raised cosine functions. In general, each choice of the phase factor θ in the projection operator gives a different set of ordinary differential equations. For θ = 0 or θ = π/2, the corresponding projection operator scheme is equivalent to the Lagrangian variation method or the bare approximation of the collective variable theory. We prove that because of the inherent symmetric property between the pulse parameters of a Gaussian ansätz results the same set of pulse parameters equations for any value of the generalized projection operator parameter θ. Finally we prove that after the substitution of the ansätze function, the Lagrange function simplifies to the same functional form irrespective of the ansätze used because of a special property shared by all the anätze chosen in this work.
Original languageEnglish
Pages (from-to)639-647
Number of pages9
JournalChaos, Solitons and Fractals
Volume31
Issue number3
DOIs
Publication statusPublished - 1 Feb 2007

ASJC Scopus subject areas

  • Mathematics(all)

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