Resonance simulation of the coupled nonlinear Mathieu’s equation

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 Schrödinger equation. According mentioned applications, thus, current study investigates stability behavior nonlinear-coupled MEs. The analysis coupled harmonic resonance cases imposes two solvability conditions, leads parametric nonlinear Landau equations. In addition, a super-harmonic combination presented. Solutions criteria discussed for each case. It shown that produces an unstable system. transition curves derived. Numerical calculations show excitation frequency on periodic solutions.