Love waves are surface seismic waves that propagate along the interface between two material layers, with particle motion parallel to the surface and perpendicular to propagation. Linear Love wave theory requires the wave speed to sit between the shear wave speeds of the two layers — too slow and it leaks, too fast and it doesn't confine. But real materials are nonlinear, and seismic amplitudes can be large.
This paper derives the general nonlinear shear wave equations for incompressible hyperelastic materials, valid for any strain energy function, and applies them to Love-type waves at a material interface. For the cubic Yeoh model, the equations develop cubic and quintic polynomial nonlinearities; extending to hyper-viscoelastic materials adds dispersion terms.
Full (2+1)-dimensional simulations reveal that nonlinear Love waves maintain variable speeds satisfying the linear existence condition while asymptotically approaching the larger material's wave speed over long times. The nonlinearity doesn't destroy the confinement — it modifies the speed. The wave stays trapped at the interface even when the amplitude is large enough for nonlinear terms to matter, but it gradually accelerates toward the limiting speed that linear theory predicts as an upper bound.