Canonically integrable nonlinear dynamical system of Shredinger type

Prykarpatsky Anatoliy Karolyovych; Kopych  Myroslava  Ivanivna

Prykarpatsky Anatoliy Karolyovych ^1,2 , Kopych Myroslava Ivanivna ³

¹ Department of Economic Cybernetics, Drohobych Ivan Franko state Pedagogical University, Drohobych, 82100, Ukraine

² University of Mining and Metallurgy, Krakow, 30-059, Poland

³ Department of Higher Mathematics, Lviv polytechnic national university, Lviv, 79007, Ukraine

Keywords: Shredinger type

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Abstract

Based on a manyparticle $δ$-like interaction potential and the second quantization scheme a new Shredinger type canonically integrable dynamical system is constructed. An infinite hierarchy of conservation laws is found in exact form. The gradient-holonomic algorithm is discussed subject to direct searching a Lax type representation supposed to exist for this dynamical system.

References

[1] Gesztesy F., Holden H. Journal of Physics // - 1987, - N20, - p.5157.

[2] Mitropolsky Yu.A., Bogolyubov N.N., Prykarpatsky A.K., Samoilenko V.G. Integrable dynamic systems: spectral and differential-geometric aspects // - Kyiv: Nauk. Dumka, - 1987. - 295 p.

[3] Prykarpatsky A., Mykytiuk I. Algebraic integrability of nonlinear dynamical systems on manifolds // - Netherlands: Kluwer, - 1998, - 560p.

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ACS Style: Prykarpatsky, A.K.; Kopych , M.I. Canonically integrable nonlinear dynamical system of Shredinger type. Bukovinian Mathematical Journal. 2018, 1
AMA Style: Prykarpatsky AK, Kopych MI. Canonically integrable nonlinear dynamical system of Shredinger type. Bukovinian Mathematical Journal. 2018; 1(160).
Chicago/Turabian Style: Anatoliy Karolyovych Prykarpatsky, Myroslava Ivanivna Kopych . 2018. "Canonically integrable nonlinear dynamical system of Shredinger type". Bukovinian Mathematical Journal. 1 no. 160.

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