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Analytical Solution Of The Fractal Cubic–Quintic Duffing Equation

Author

Listed:
  • ALEX ELà AS-ZÚÑIGA

    (Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Avenida Eugenio Garza Sada 2501, Monterrey 64849, Mexico)

  • LUIS MANUEL PALACIOS-PINEDA

    (Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Avenida Eugenio Garza Sada 2501, Monterrey 64849, Mexico†Tecnológico Nacional de México/Instituto, Tecnológico de Pachuca, Carr. México-Pachuca Km, 87.5, Pachuca, Hidalgo, Código Postal 42080, Mexico)

  • ISAAC H. JIMÉNEZ-CEDEÑO

    (Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Avenida Eugenio Garza Sada 2501, Monterrey 64849, Mexico)

  • OSCAR MARTÃ NEZ-ROMERO

    (Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Avenida Eugenio Garza Sada 2501, Monterrey 64849, Mexico)

  • DANIEL OLVERA-TREJO

    (Mechanical Engineering and Advanced Materials Department, School of Engineering and Science, Tecnologico de Monterrey, Avenida Eugenio Garza Sada 2501, Monterrey 64849, Mexico)

Abstract

In this work, the fractal cubic–quintic Duffing’s equation analytical solution is obtained using the two-scale transform and elliptic functions. Then, the analytical solution is used to study wave propagation in a fractal medium. Since the value of the fractal parameter adjusts the pulse frequency and wavelength propagation velocity, depending upon the fractal medium physical properties, it is found that the information contained in the pulse can be carried out faster over long distances without distortion or loss of intensities.This paper offers a new light on the applicability of the two-scale transform of fractal theory to comprehend natural phenomena.

Suggested Citation

  • Alex Elã As-Zãšã‘Iga & Luis Manuel Palacios-Pineda & Isaac H. Jimã‰Nez-Cedeã‘O & Oscar Martã Nez-Romero & Daniel Olvera-Trejo, 2021. "Analytical Solution Of The Fractal Cubic–Quintic Duffing Equation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-7, June.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:04:n:s0218348x21500808
    DOI: 10.1142/S0218348X21500808
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