Integrable (1+1)-dimensional systems and the Riemann problem with a shift

L. V. Bogdanov, Vladimir E Zakharov

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish (US)
Article number004
Pages (from-to)817-835
Number of pages19
JournalInverse Problems
Volume10
Issue number4
DOIs
StatePublished - 1994
Externally publishedYes

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Cauchy problem
Cauchy Problem
Scattering
differential operators
Inverse Scattering Problem
Boussinesq Equations
Continuous Spectrum
shift
continuous spectra
inverse scattering
Integrable Systems
Differential operator
First-order
Invariant
Line
Arbitrary

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 journalArticle

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