This work is to explore the time-reversal symmetry breaking employing an acoustic wave platform through space-time parametric modulations, for the purpose of developing nonlinear devices such as amplifiers and mixers. The strength of acoustic wave platform is that it can obtain great leverage on the slow velocity and small wavelength of acoustic waves at RF to minimize the footprint of transmission lines. To realize parametric amplification, nonlinear Surface Acoustic Wave(SAW) grating is employed to pump a dynamic biasing electric field into the piezoelectric material to couple the pump electromagnetic wave to the propagating surface acoustic waves in the condition of phase matched. Two different ways to achieve nonlinear change of piezoelectric coefficient and elastic stiffness are proposed: 1) Material nonlinearity using ferromagnetic material like BST; 2) Geometrical nonlinearity using the coupling between vertical and parallel stiffness. The fractional modulation of elastic stiffness is approximate 4% in the first approach and can reach 10% or even higher in the second approach. Simulation validation using COMSOL demonstrates the parametric fixing effects produced on the Surface Acoustic Wave devices. Fabrication and characterization of Surface Acoustic Wave delay lines are also provided.