Abstract:
A new gradient-holonomic approach to the construction of integrability criteria for
nonlinear dynamical systems is described for the example of the nonlinear hydrodynamic equations in the mechanics of Ito and of Benney and Kaup.
Citation:
N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, “Complete integrability of the nonlinear ito and Benney–Kaup systems: Gradient algorithm and lax representation”, TMF, 67:3 (1986), 410–425; Theoret. and Math. Phys., 67:3 (1986), 586–596
\Bibitem{BogPri86}
\by N.~N.~Bogolyubov (Jr.), A.~K.~Prikarpatskii
\paper Complete integrability of the nonlinear ito and Benney--Kaup systems: Gradient algorithm and lax representation
\jour TMF
\yr 1986
\vol 67
\issue 3
\pages 410--425
\mathnet{http://mi.mathnet.ru/tmf5087}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=858812}
\zmath{https://zbmath.org/?q=an:0623.35061}
\transl
\jour Theoret. and Math. Phys.
\yr 1986
\vol 67
\issue 3
\pages 586--596
\crossref{https://doi.org/10.1007/BF01028694}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1986F672900007}
Linking options:
https://www.mathnet.ru/eng/tmf5087
https://www.mathnet.ru/eng/tmf/v67/i3/p410
This publication is cited in the following 11 articles:
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Anatolij K. Prykarpatski, Victor A. Bovdi, Myroslava I. Vovk, Petro Ya. Pukach, “On parametric generalizations of the Kardar-Parisi-Zhang equation and their integrability”, J. Phys.: Conf. Ser., 2667:1 (2023), 012043
Anatolij Prykarpatski, Petro Pukach, Myroslava Vovk, “Symplectic Geometry Aspects of the Parametrically-Dependent Kardar–Parisi–Zhang Equation of Spin Glasses Theory, Its Integrability and Related Thermodynamic Stability”, Entropy, 25:2 (2023), 308
Anatolij K. Prykarpatski, Petro Ya. Pukach, Myroslava I. Kopych, Trends in Mathematics, Geometric Methods in Physics XXXIX, 2023, 233
Anatolij K. Prykarpatski, “Quantum Current Algebra in Action: Linearization, Integrability of Classical and Factorization of Quantum Nonlinear Dynamical Systems”, Universe, 8:5 (2022), 288
Anatolij K. Prykarpatski, “On symmetry analysis of differential systems on functional manifolds”, Journal of Mathematical Analysis and Applications, 490:2 (2020), 124326
D. Blackmore, A. K. Prykarpatsky, E. Özçağ, K. Soltanov, “Integrability Analysis of a Two-Component Burgers-Type Hierarchy”, Ukr Math J, 67:2 (2015), 167
Ivanov, R, “Two-component integrable systems modelling shallow water waves: The constant vorticity case”, Wave Motion, 46:6 (2009), 389
Tsuchida, T, “Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I”, Journal of Physics A-Mathematical and General, 38:35 (2005), 7691
N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, “Quantum current lie algebra as the universal algebraic structure of the symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics”, Theoret. and Math. Phys., 75:1 (1988), 329–339
V. K. Krivoshchekov, A. A. Slavnov, L. O. Chekhov, “Effective Lagrangian for supersymmetric quantum chromodynamics and the problem of dynamical breaking of supersymmetry”, Theoret. and Math. Phys., 72:1 (1987), 686–693
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