Abstract
The connection between scale invariant wave functions and solutions of some nonlinear equations (e.g., solitons and compactons) has been studied. Scale invariant functions are 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.
| Original language | American English |
|---|---|
| Journal | International Journal of Modern Physics E |
| Volume | 7 |
| State | Published - 1998 |
| Externally published | Yes |
Keywords
- Hamiltonian systems
- wavelets
- multi-scale
- scalings
- finite differences
Disciplines
- Non-linear Dynamics
- Numerical Analysis and Computation
- Ordinary Differential Equations and Applied Dynamics
- Physics