The SDIFF(T2)local-generalized Kac-Moody G(T2) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the
We numerically study the propagation, reflection and collision of soliton-like pulses in the vertical granular chain under gravity. For the pure granular chain
Taking into account the quantum size effects and considering three types of scattering from bulk impurities,rough surface and rough interfaces, we use quantum-s