Constant amplitude acceleration waves in a prestrained incompressible isotropic elastic solid

It is known that all transverse plane acceleration waves that propagate through a homogeneously deformed Mooney-Rivlin material do so without a change in amplitude. Here it is shown that the Mooney-Rivlin material is the only incompressible isotropic hyperelastic material that permits transverse plane acceleration waves to propagate in any direction without a change in amplitude, regardless of the homogeneous prestrain.