Dynamics of Patterns on Elastic Hypersurfaces. Part II. Wave Mechanics of Flexural Quasi-Particles

In the first part of this work, the shear wave phenomena in an elastic 3D continuum are investigated and an analogy to Maxwellian electrodynamics is shown. In the present part, the model is extended assuming the continuum to be a momentum-supporting hypersurface in 4D space (a hypershell). The transverse (flexural) deformations of the shell are governed by a Generalized Nonlinear Dispersive Wave Equation (GDWE) of Schrödinger type. The Hamiltonian structure of the model is discussed. The solitary wave solutions are shown to fit the concept of quasi-particles. The concept of pseudo-mass is introduced and the Newtonian mechanics for the centers of quasiparticles/solitons is derived. Numerical examples of the shapes in 2D are presented. The presence of attractive force between the localized elevations of the surface is discussed and shown to depend on the distance between them as | x|−2.