Stability of self-resonance mechanisms in nonlinear interaction between two primary harmonic waves

In the present work the stability criterion for two coupled nonlinear Schrödinger equations having parametric terms is derived. In this investigation, two different types of coupled nonlinear Schrödinger equations are discussed. Two coupled parametric nonlinear Schrödinger equations govern the wave behavior at the self-secondary resonance interaction and other two coupled parametric equations describe the wave-wave interaction at self-cubic resonance case. Stability criterion governing resonance mechanisms is performed in view of temporal periodic perturbations. Moreover, stability criterion at the perfect resonance case is achieved. Further, some numerical calculations are made to screen the stability pictures at the self-second resonance case.