Author(s)

Fawzy Mohamed Fahmy El-Sabaa, Alshimaa Abdelbasit Mohamed^*, Salma Khalel Zakria

Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt.

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.

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

Fahmy El-Sabaa, F. , Mohamed, A. and Zakria, S. (2017) The Qualitative and Quantitative Methods of Kovalevskys Case. Journal of Applied Mathematics and Physics, 5, 1837-1854. doi: 10.4236/jamp.2017.59155.