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The Love surface-acoustic wave seen as a guided non-Newtonian quasi-particle

Following along the line of recent works, the paper introduces the notion of quasi-particles that are associated with surface-acoustic waves of the Love type via the canonical conservation laws of Noether’s theory of invariants. The strange point mechanics (velocity-dependent “mass” and energy) is obtained by integrating the conservation laws of “wave momentum” and energy over an element of volume representative of the wave motion. This original but involved point mechanics obtained for the quasi-particle is neither Newtonian nor Lorentzian because of the existence of surface waves restricted to a bounded interval of velocities that is characteristic of Love waves. The reduction of this description to the cases of an isolated elastic layer of finite thickness with pure shear horizontal motion and of the so-called Murdoch case corresponding to a thin-film approximation (half-space with an upper material boundary equipped with mass and surface elasticity) studied independently is exactly proved.