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 - 1994 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematical Physics
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Applied Mathematics
Cite this
Integrable (1+1)-dimensional systems and the Riemann problem with a shift. / Bogdanov, L. V.; Zakharov, Vladimir E.
In: Inverse Problems, Vol. 10, No. 4, 004, 1994, p. 817-835.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Integrable (1+1)-dimensional systems and the Riemann problem with a shift
AU - Bogdanov, L. V.
AU - Zakharov, Vladimir E
PY - 1994
Y1 - 1994
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0006065293&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0006065293&partnerID=8YFLogxK
U2 - 10.1088/0266-5611/10/4/004
DO - 10.1088/0266-5611/10/4/004
M3 - Article
AN - SCOPUS:0006065293
VL - 10
SP - 817
EP - 835
JO - Inverse Problems
JF - Inverse Problems
SN - 0266-5611
IS - 4
M1 - 004
ER -