The $$\left( \frac{\boldsymbol{G}^{\prime }}{\boldsymbol{G}},\frac{\boldsymbol{1}}{\boldsymbol{G}}\right)$$ G ′ G , 1 G -expansion method and its applications for constructing many new exact solutions of the higher-order nonlinear Schrödinger equation and the quantum Zakharov–Kuznetsov equation