Making use of the link with Schrodinger operators and the Darboux transformation, a Backlund transformation BT for Β¨Ε½ . the continuous Ermakov-Pinney equation is constructed. By considering two applications of the BT we obtain a second order discrete equation, which is naturally interpreted as the e
β¦ LIBER β¦
A discrete Pinney equation
β Scribed by W.K. Schief
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 166 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
β¦ Synopsis
The classical Pinney equation is discretised in such a way that its well-known nonlinear superposition principle is preserved. Thus, the general solution of the discrete Pinney equation is given in terms of two linearly independent solutions of a discrete SchrSdinger equation.
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