Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON SOME NEW SOLITONS SOLUTIONS OF NONLINEAR COMPLEX GINZBURG-LANDAU EQUATION SOLVED BY MODIFIED JACOBI ELLIPTIC FUNCTIONS METHOD

  • Received : 2023.09.01
  • Accepted : 2023.12.31
  • Published : 2024.03.30
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Abstract

This article explains how solitons propagate when there is a detuning factor involved. The explanation is based on the nonlinear complex Ginzburg-Landau equation, and we first consider this equation before systematically deriving its solutions using Jacobian elliptic functions. We illustrate that one specific ellipticity modulus is on the verge of occurring. The findings from this study can contribute to the understanding of previous research on the Ginzburg-Landau equation. Additionally, we utilize Jacobi's elliptic functions to define specific solutions, especially when the ellipticity modulus approaches either unity or zero. These solutions correspond to particular periodic wave solitons, which have been previously discussed in the literature.

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References

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