https://doi.org/10.1140/epjs/s11734-023-00861-1
Regular Article
Fractal representation of tsunami waves: a generalized geophysical gardner equation
1
Department of Computer Science and Engineering, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Rangpo, 737136, East-Sikkim, India
2
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, 632014, Vellore, Tamil Nadu, India
3
College of Electrical and Information Engineering, Hunan University, 410082, Changsha, Hunan, China
4
Department of Electronics and Communication Engineering, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Rangpo, East Sikkim, 737136, Majitar, India
5
Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Rangpo, 737136, East-Sikkim, India
Received:
14
January
2023
Accepted:
3
May
2023
Published online:
5
June
2023
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 (
), 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 (). Perturbed tsunami waves show quasiperiodic and chaotic nature based on suitable values of the Coriolis parameter (). 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.
Framework of Fractals in Data Analysis: Theory and Interpretation. Guest editors: Santo Banerjee, A. Gowrisankar.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
