Abstract
We study (1+1)-dimensional integrable systems considering them as special cases of the more general (2+1)-dimensional systems. Using the non-local delta -problem approach in (2+1) dimensions, we show that the delta -problem with a shift and (for the decreasing solutions) the Riemann problem with a shift arise naturally in (1+1) dimensions. The Boussinesq equation and the first-order relativistically-invariant systems are investigated. The approach developed also allows us to investigate the structure of the continuous spectrum and the inverse scattering problem for an arbitrary-order ordinary differential operator on the infinite line.
| Original language | English (US) |
|---|---|
| Article number | 004 |
| Pages (from-to) | 817-835 |
| Number of pages | 19 |
| Journal | Inverse Problems |
| Volume | 10 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 1 1994 |
| Externally published | Yes |
ASJC Scopus subject areas
- Theoretical Computer Science
- Signal Processing
- Mathematical Physics
- Computer Science Applications
- Applied Mathematics
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Bogdanov, L. V., & Zakharov, V. E. (1994). Integrable (1+1)-dimensional systems and the Riemann problem with a shift. Inverse Problems, 10(4), 817-835. [004]. https://doi.org/10.1088/0266-5611/10/4/004