Abstract: This theoretical report is pertinent to the mathematical problem of finding of all the possible eigenvectors for the fourpotential shear-horizontal surface acoustic wave (4P-SH-SAW) propagation in suitable solids. In this case, the wave propagation is coupled with the four potentials, i.e. the electrical, magnetic, gravitational, and cogravitational ones. The taking into account these four potentials results in significant difficulties to find any eigenvector because the mathematical method is significantly complicated. To find all suitable eigenvectors is very important here because it will allow one in the future to theoretically disclose all suitable solutions of acoustic waves. This is applicable to the problem of finding of propagation velocities of the SH-SAWs, interfacial SH-waves, plate SH-waves, and more complicated cases. It is thought that all the effects (for instance, the gravitocogravitic, gravitoelectric, cogravitoelectric, gravitomagnetic, cogravitomagnetic effects) individually or collaboratively participating in the acoustic wave propagation can be vital for acoustic wave propagation that can be readily used for constitution of suitable technical devices. This fact must be first demonstrated theoretically for experimentalists and engineers working with the transmitting, detecting, and converting of the electromagnetic waves’ signals. It is expected that the future communication technologies will also exploit gravitational waves for the new communication era based on some gravitational phenomena.