TY - JOUR

T1 - New fractional nonlinear integrable Hamiltonian systems

AU - Hentosh, Oksana Ye

AU - Kyshakevych, Bohdan Yu

AU - Blackmore, Denis

AU - Prykarpatski, Anatolij K.

N1 - Funding Information:
The authors are indebted to Profs. Jan Cieśliński (Białystok University, Poland) and Jan Koroński (Kraków University of Technology, Poland) for their instrumental comments and remarks which were very useful during preparation of the manuscript. Also, A.K.P. warmly acknowledges the Institute of Mathematics at the Cracow Polytechnical University for a local research grant F-2/370/2018/DS .
Publisher Copyright:
© 2018 Elsevier Ltd

PY - 2019/2

Y1 - 2019/2

N2 - 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.

AB - 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.

KW - Ad-invariant trace-functional

KW - Adler–Kostant–Symes approach

KW - Casimir invariants

KW - Fractional Korteweg–de Vries type equations

KW - Fractional nonlinear Schrödinger type equations

KW - Fractional pseudo-differential metrized operator Lie algebra

KW - Fractional symbolic metrized functional Lie algebra

KW - Lie–Poisson structure

KW - R-structure

UR - http://www.scopus.com/inward/record.url?scp=85052904233&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052904233&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2018.08.009

DO - 10.1016/j.aml.2018.08.009

M3 - Article

AN - SCOPUS:85052904233

SN - 0893-9659

VL - 88

SP - 41

EP - 49

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -