Demonstration Systems for Kink-Solitons

Abstract

We consider a mechanical lattice where the basic oscillating units experience a double-well on-site potential, and are linearly and nonlinearly coupled. In the continuum limit the lattice equations can be approximated by a nonlinear partial differential equation. With nonlinear coupling only, this equation exhibits a static kink solution with a compact shape or compacton. When both linear and nonlinear coupling exist, one can obtain a dynamic compacton solution propagating at the characteristic velocity of linear waves. Contrary to the static compacton solution, which is stable, the dynamic compacton is unstable: it looses progressively its compact shape as it propagates, and evolves into a kink waveform. A nice feature is that mechanical analogs of this lattice can be constructed that allow one to observe kinks. We constructed two mechanical lattices: one with torsion and gravity pendulums and another one with flexion and gravity oscillating units. Both experimental systems allow one to illustrate and study qualitatively the dynamical properties of the propagating kinks. In the strong nonlinear coupling limit static compactons can be created. In the weak coupling limit, lattice effects and the observation of discrete kinks are briefly considered.