On a class of systems of equations of the Lax type

Authors

  • A. A. Lunyov
  • E. V. Oliynyk

DOI:

https://doi.org/10.15407/dopovidi2015.01.025

Keywords:

equation of the Lax type, non-linear system, operator

Abstract

The non-linear system of equations of the Lax type is investigated. It is a basis of the triangular models for commutative systems of linear non-self-adjoint operators. In some cases, the complete description of solutions of this system is found.

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References

Zolotarev V. A. Analytical methods of spectral and non-unitary representations of non-selfadjoint operators, Kharkov: Izd-vo KhNU im. V. N. Karazina, 2003.

Zolotarev V. A. Teoriia funktsii, funktsion analiz i ikh prilozheniia. Resp. sb., 1983, Vol. 40: 68–71 (in Russian).

Zolotarev V. A. Mat. sb., 1990, 181, No 7: 965–994 (in Russian).

Livshits M. S., Yantsevich A. A. The theory of operator nodes in Hilbert spaces, Kharkov: Izd-vo Khark. Univ., 1971 (in Russian).

Lunev A. A., Oleinik E. V. Ukr. mat. visn., 2013, 10, No 4: 507–531 (in Russian).

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Published

08.01.2025

How to Cite

Lunyov, A. A., & Oliynyk, E. V. (2025). On a class of systems of equations of the Lax type . Reports of the National Academy of Sciences of Ukraine, (1), 25–30. https://doi.org/10.15407/dopovidi2015.01.025

Issue

No. 1 (2015): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

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