Hamiltonian system and symmetries for scale invariant wavefunctions
The connection between scale invariant wavefunctions and solutions of some nonlinear equations (e.g., solitons and compactons) have been studied. Scale invariant functions axe shown to have variational properties and a nonlinear algebraic structure. Any two-scale equation follows from Hamilton's equation of an infinite-dimensional Hamiltonian system, providing a self-similar formalism that is useful in studies of hierarchical and nonlinear lattices, soliton and compacton waves. The algebraic structure of any scaling function is shown to be a deformation of the trigonometric series generating algebra.