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Fractal representation of tsunami waves: a generalized geophysical gardner equation

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Abstract

Dynamical properties of tsunami waves for the generalized geophysical Gardner equation (GGGE) are investigated through phase plane analysis. Using Galilean transformation, the GGGE is transformed to a conservative Hamiltonian system. Existence of linear and supernonlinear tsunami waves is reported through phase portrait and time series analysis. A collection of necessary conditions is obtained for the existence of such kinds of waves for the GGGE. Analytical forms of various types of tsunami waves for GGGE are presented and effects of physical parameters on such waves are discussed. The Coriolis parameter (\(\omega _0\)), and velocity (v) of traveling waves have consequential effects on the nonlinear and supernonlinear tsunami waves. Perturbed tsunami waves are studied using phase projections and time series plots considering different values of the Coriolis parameter (\(\omega _0\)). Perturbed tsunami waves show quasiperiodic and chaotic nature based on suitable values of the Coriolis parameter (\(\omega _0\)). Further, the phase portraits and time series plots of the perturbed tsunami waves are reconstructed using the fractal interpolation technique to manifest their hidden self-similar nature.

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Acknowledgements

All authors are thankful to the reviewers for their constructive and invaluable suggestions for improving the quality of the manuscript. Asit Saha is thankful to SMIT (SMU) for providing research funding (Ref. Nos. 6100/ SMIT/ R &D/ Project/ 26/ 2019).

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Rangpo, East-Sikkim, 737136, India

    Aranya Jha

  2. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, 632014, India

    A. Gowrisankar

  3. College of Electrical and Information Engineering, Hunan University, Changsha, 410082, Hunan, China

    Shaobo He

  4. Department of Electronics and Communication Engineering, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Rangpo, East Sikkim, 737136, India

    Harshvardhan Anand

  5. Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Rangpo, East-Sikkim, 737136, India

    Asit Saha

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  1. Aranya Jha
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Correspondence to Asit Saha.

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Framework of Fractals in Data Analysis: Theory and Interpretation. Guest editors: Santo Banerjee, A. Gowrisankar.

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Jha, A., Gowrisankar, A., He, S. et al. Fractal representation of tsunami waves: a generalized geophysical gardner equation. Eur. Phys. J. Spec. Top. 232, 979–990 (2023). https://doi.org/10.1140/epjs/s11734-023-00861-1

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