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Ali Ahmad, T. (2011) New Generalized Jacobi Elliptic Function Rational Expansion Method. Journal of Computation and Applied Mathematics, 235, 4117-4127.
https://doi.org/10.1016/j.cam.2011.03.002

has been cited by the following article:

• TITLE: Six New Sets of the Non-Elementary Jef-Family-Functions that Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs

  AUTHORS: Magne Stensland

  KEYWORDS: Non-Elementary Functions, Second-Order Nonlinear Autonomous ODE, Limit Cycle

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.4, April 28, 2023

  ABSTRACT: In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.