Abstract
We introduce a generalized similarity analysis which grants a qualitative description of the localized solutions of any nonlinear differential equation. This procedure provides relations between amplitude, width, and velocity of the solutions, and it is shown to be useful in analyzing nonlinear structures like solitons, doublets, triplets, compact supported solitons and other patterns. We also introduce kink- antikink compact solutions for a nonlinear-nonlinear dispersion equation, and we construct a basis of finite wavelength functions having self-similar properties.
| Original language | American English |
|---|---|
| Journal | International Journal of Modern Physics E |
| Volume | 9 |
| State | Published - 2000 |
| Externally published | Yes |
Keywords
- Solitons
- kink
- compacton
- compact support
- wavelet
- scaling
- nonlinear equations
Disciplines
- Dynamical Systems
- Harmonic Analysis and Representation
- Non-linear Dynamics
- Other Physics
- Partial Differential Equations