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New Jacobi Elliptic Solutions and Other Solutions in Optical Metamaterials Having Higher-Order Dispersion and Its Stability Analysis

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Abstract

In this paper, we investigate the nonlinear Schrödinger equation in metamaterials having cubic-quintic nonlinearity with third and fourth order dispersions. Two effective techniques, namely, the new extended auxiliary equation method and the extended Kudryashov method are utilized to find the Jacobi elliptic functions solutions and other solutions to this model. The Jacobi elliptic functions solutions are degenerated to bright, dark, singular, and periodic solitary wave solutions. In addition, the condition for the modulational instability of continuous wave solutions for the equation is generated. The characteristics of the obtained solitons are analyzed via several 3D and 2D graphics.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jaffna, Jaffna, Sri Lanka

    Thilagarajah Mathanaranjan

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  1. Thilagarajah Mathanaranjan
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Mathanaranjan, T. New Jacobi Elliptic Solutions and Other Solutions in Optical Metamaterials Having Higher-Order Dispersion and Its Stability Analysis. Int. J. Appl. Comput. Math 9, 66 (2023). https://doi.org/10.1007/s40819-023-01547-x

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