El Naschie’s Cantorian space time, Toda lattices and Cooper–Agop pairs

We show that space time–matter connection works like a quasiautonomous structure by means of cnoidal oscillation modes. Identifying the cnoidal oscillation modes with one-dimensional Toda lattice, by its nonlinear mode works, on the acoustic branch of the phononic spectrum, generalized Cooper pairs (“Cooper–Agop pairs”) are induced. In such a context the fractal characteristic is given by redefining a coefficient in a Korteweg–de Vries (KdV) type equation, and the Cantorian structure are assimilated with two coupled oscillator like in the simple mechanical model of El Naschie’s ε(∞) theory.