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

L. V. Bogdanov, Vladimir E Zakharov

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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
Publication statusPublished - 1994
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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