Abstract Avoided crossings of level pairs with opposite slopes can form potential-energy minima for the external degree freedom quantum particles, giving rise to metastable states on avoided (MSACs). Nonadiabatic decay MSACs is studied by solving two-component Schrödinger equation in diabatic and adiabatic representations. Non-perturbative lifetime values are found evaluating wave function flux...

In this study, we obtained some exact solutions of the coupled non-linear Helmholtz equation through sub-equation method. The were hyperbolic and trigonometric. We observed MATHEMATICA 11.2 that these provided equations, presented graphs in last section.