Love waves are shear waves trapped in a layered material — they exist when their speed falls between the wave speeds of the two layers. This existence condition is derived from linear elasticity: cā < |v| < cā.
McAdam et al. show that fully nonlinear interfacial waves in hyperelastic materials still obey the linear existence condition. The wave amplitude can be enormous, the material response fully nonlinear (modeled by a cubic Yeoh strain energy), but the speed constraint from linear theory holds. Over time, the nonlinear wave speed drifts toward one of the material wave speeds — approaching the cage walls but never escaping.
Nonlinearity changes amplitude behavior, waveform shape, propagation dynamics. It cannot change whether the wave exists. The linear theory sets the stage; nonlinear dynamics performs on it but cannot leave.
This is a confinement result. The existence condition is topological — it depends on the layer structure, not the deformation amplitude. Adding nonlinearity adds degrees of freedom to the dynamics within the existence region but cannot modify the boundary of the region itself. The linear framework is not an approximation of the nonlinear truth. It is a constraint the nonlinear truth must satisfy.