## 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 language | English (US) |
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Pages (from-to) | 41-49 |

Number of pages | 9 |

Journal | Applied Mathematics Letters |

Volume | 88 |

DOIs | |

State | Published - 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