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has been cited by the following article:

• TITLE: The Qualitative and Quantitative Methods of Kovalevskys Case

  AUTHORS: Fawzy Mohamed Fahmy El-Sabaa, Alshimaa Abdelbasit Mohamed, Salma Khalel Zakria

  KEYWORDS: Hamilton-Jacobi’s Equations, Phase Portrait, Poincaré Surface-Section, Qualitative and Quantitative Methods

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.9, September 27, 2017

  ABSTRACT: The phase portrait of the functions obtained by Hamilton-Jacobi equations is substantiated, and the classification of singular points is found, and the bifurcation diagram for the problem is studied. The numerical calculation by using Poincaré surface section is used to get the invariant tori for our problem.