Resonance simulation of the coupled nonlinear Mathieu’s equation
Source abstract
Abstract
Numerous theoretical physics and chemistry problems can be modeled using Mathieu’s equations (MEs). They are crucial to the theory of potential energy in quantum systems, which is equivalent to the Schrödinger equation. According to the mentioned applications, thus, the current study investigates the stability behavior of the nonlinear-coupled MEs. The analysis of the coupled harmonic resonance cases imposes two coupled solvability conditions, which leads to coupled parametric nonlinear Landau equations. In addition, a super-harmonic nonlinear resonance combination is presented. Solutions and stability criteria are discussed for each case. It is shown that resonance produces an unstable system. The transition curves are derived. Numerical calculations show the excitation of the frequency on the periodic solutions.
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Research context
OpenAlex topics: Nonlinear Photonic Systems · Fractional Differential Equations Solutions · Quantum Mechanics and Non-Hermitian Physics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy 1 , Cairo, Egypt
Department of Physics, College of Science, Princess Nourah bint Abdulrahman University 2 , P.O. Box 84428, Riyadh 11671, Saudi Arabia
3 Faculty of Sciences, University of Maroua, P.O. Box 814, Maroua, Cameroon
Department of Physics, Faculty of Science, Port Said University 4 , Port Said 42521, Egypt
Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University 5 , Al-Baha 1988, Saudi Arabia
Funding
Princess Nourah bint Abdulrahman University
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