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https://doi.org/10.1175/2008JAS2539.1

has been cited by the following article:

• TITLE: Finding the Fibonacci Spiral Patterns in Atmospheric Equatorial Waves

  AUTHORS: Ranis Ibragimov, Eleanor Blake

  KEYWORDS: Atmospheric Waves, Fibonacci Sequence, Shallow Water Theory, Exact Solutions

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.12, December 29, 2022

  ABSTRACT: The purpose of this paper is to analyze and visualize the exact invariant solution of the nonlinear simplified version of the shallow water equations which are being used to simulate equatorial atmospheric waves of planetary scales. The method of obtaining the exact solution is based on the Lie group invariance principle. It is shown that the obtained invariant solution has a Fibonacci spiral-like form and has two parameters k and t0. We have defined a new model hypermarameter Δkt = t – t0, where t is time. The question of particular interest is: can we tune the hypermarameter in order to match the exact solution to the actual Fibonacci spiral? It was discovered that the physically relevant part of the solution matches exactly the Fibonacci spiral.