New fractional nonlinear integrable Hamiltonian systems

Oksana Ye Hentosh, Bohdan Yu Kyshakevych, Denis Blackmore, Anatolij K. Prykarpatski

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We have constructed a new fractional pseudo-differential metrized operator Lie algebra on the axis, enabling within the general Adler–Kostant–Symes approach the generation of infinite hierarchies of integrable nonlinear differential-fractional Hamiltonian systems of Korteweg–de Vries, Schrödinger and Kadomtsev–Petviashvili types. Using the natural quasi-classical approximation of the metrized fractional pseudo-differential operator Lie algebra, we construct a new metrized fractional symbolic Lie algebra and related infinite hierarchies of integrable mutually commuting fractional symbolic Hamiltonian flows, modeling Benney type hydrodynamical systems.

Original languageEnglish (US)
Pages (from-to)41-49
Number of pages9
JournalApplied Mathematics Letters
Volume88
DOIs
StatePublished - Feb 2019

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Keywords

  • Ad-invariant trace-functional
  • Adler–Kostant–Symes approach
  • Casimir invariants
  • Fractional Korteweg–de Vries type equations
  • Fractional nonlinear Schrödinger type equations
  • Fractional pseudo-differential metrized operator Lie algebra
  • Fractional symbolic metrized functional Lie algebra
  • Lie–Poisson structure
  • R-structure

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