Generalized fractional bi-Hamiltonian structure of Plebański's second heavenly equation in terms of conformable fractional derivatives

YAZICI D., Topuz S.

Journal of Computational and Applied Mathematics, vol.452, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 452
  • Publication Date: 2024
  • Doi Number: 10.1016/j.cam.2024.116121
  • Journal Name: Journal of Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Bi-Hamiltonian, Conformable derivative, Magri's theorem, Second heavenly equation, Symplectic structure
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we propose a symplectic and bi-Hamiltonian structure to a generalized (3+1) -dimensional Plebański's second heavenly (SH) equation by using a conformable fractional derivative. We write the SH equation in terms of conformable fractional derivatives by replacing classical time (t) and space (z) derivatives with conformable fractional derivatives. We name this equation as a conformable fractional second heavenly (CFSH) equation and cast it in a two-component evolutionary form. We construct a degenerate Lagrangian for a two-component conformable fractional system and find a new Euler–Lagrange formalism for four-dimensional Lagrange density. We apply Dirac's theory of constraints to the CFSH equation and we prove that it admits bi-Hamiltonian structure according to Magri's theorem.