Wavelets generated by Riesz potentials of KdV solitons
Abstract
In recent years the study of wavelets gained much popularity among mathematicians and applied scientists. It firmly established itself in the field of series and integral expansions and signal processing and led to new and interesting applications. Our interest in this article stems from finding a completely new representative of wavelets, the one coming from the fractional derivative of Korteweg–de Vries solitons. More precisely, we mean by this Riesz fractional derivatives of the well-known KdV solitons. The Riesz fractional derivative and its conjugate are given via the Hilbert transform.
- Publication:
-
Analysis and Mathematical Physics
- Pub Date:
- December 2012
- DOI:
- 10.1007/s13324-012-0049-y
- Bibcode:
- 2012AnMP....2..325V
- Keywords:
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- Fractional Derivative;
- Soliton Solution;
- Functional Differential Equation;
- Mother Wavelet;
- Riemann Zeta Function