Solutions by Quadratures of Complex Bernoulli Differential Equations and Their Quantum Deformation

  1. Campoamor-Stursberg, Rutwig 33
  2. Fernández-Saiz, Eduardo 1
  3. Herranz, Francisco J. 2
  1. 1 Department of Quantitative Methods, CUNEF Universidad, E-28040 Madrid, Spain
  2. 2 Universidad de Burgos
    info

    Universidad de Burgos

    Burgos, España

    ROR https://ror.org/049da5t36

  3. 3 Universidad Complutense de Madrid
    info

    Universidad Complutense de Madrid

    Madrid, España

    ROR 02p0gd045

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Journal:
Axioms

ISSN: 2075-1680

Year of publication: 2023

Volume: 13

Issue: 1

Pages: 26

Type: Article

DOI: 10.3390/AXIOMS13010026 GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Axioms

Abstract

It is shown that the complex Bernoulli differential equations admitting the supplementary structure of a Lie–Hamilton system related to the book algebra �2 can always be solved by quadratures, providing an explicit solution of the equations. In addition, considering the quantum deformation of Bernoulli equations, their canonical form is obtained and an exact solution by quadratures is deduced as well. It is further shown that the approximations of ��ℎ-order in the deformation parameter from the quantum deformation are also integrable by quadratures, although an explicit solution cannot be obtained in general. Finally, the multidimensional quantum deformation of the book Lie–Hamilton systems is studied, showing that, in contrast to the multidimensional analogue of the undeformed system, the resulting system is coupled in a nontrivial form.

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