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Analytic solution of the system of two coupled differential equations with the fifth-order non-linearity

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  • Cveticanin, L.

Abstract

In this paper an approximate method for solving a system of two coupled second-order non-linear differential equation with strong and weak non-linearity is developed. The strong non-linearities are of the third and of the fifth order. The suggested new method is partially based on the elliptic-Krylov–Bogolubov method and on the power series method developed for solving the weak non-linear differential equations. The one-frequency solution is considered for the case of certain relations between the equation parameters p and m, and initial conditions. As a special case the oscillatory motion of the physical system described with a fourth-order strong non-linear differential equation is considered. A wide analysis of the corresponding equation is done. The results of the suggested analytic procedure are compared with numerical ones. They show a good agreement.

Suggested Citation

  • Cveticanin, L., 2003. "Analytic solution of the system of two coupled differential equations with the fifth-order non-linearity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(1), pages 83-94.
    • Handle: RePEc:eee:phsmap:v:317:y:2003:i:1:p:83-94
    DOI: 10.1016/S0378-4371(02)01323-7
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    References listed on IDEAS

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    1. Mahmoud, Gamal M. & Aly, Shaban A.H., 2000. "On periodic solutions of parametrically excited complex non-linear dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(3), pages 390-404.
    2. Cveticanin, L., 2001. "Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(3), pages 348-360.
    3. Mahmoud, Gamal M., 1998. "Approximate solutions of a class of complex nonlinear dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 253(1), pages 211-222.
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    Cited by:

    1. Stylianos Vasileios Kontomaris & Georgios Chliveros & Anna Malamou, 2023. "Approximate Solutions for Undamped Nonlinear Oscillations Using He’s Formulation," J, MDPI, vol. 6(1), pages 1-12, February.
    2. Weaam Alhejaili & Alvaro H. Salas & Samir A. El-Tantawy, 2022. "Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators," Mathematics, MDPI, vol. 10(23), pages 1-13, November.
    3. Weaam Alhejaili & Alvaro H. Salas & Samir A. El-Tantawy, 2023. "Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators," Mathematics, MDPI, vol. 11(9), pages 1-12, April.

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