For the fist time the analytic solution of the task of longitudinal acoustic-electric waves spreading in multi-layer AlGaN/GaN heterostructures has been found. If the thicknesses of heterostructure layers are significantly smaller than the wave length, an exact equation transforms to the Love-tip waves one. The obtained results can be easily generalized for multi-layer heterostructures. If the thickness of each layer is much smaller than the wave thickness, then its phase velocity and the propagation parameters will depend on the substrate piezo-electric parameters and the heterolayer directly contacting with it.