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
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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 -