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Examples of Completely Integrable Bateman Pairs

In: Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics

Author

Listed:
  • Robert L. Anderson

    (UGA, Department of Physics and Astronomy)

  • Piotr W. Hebda

    (Reinhardt College, Math and Science Division)

  • Guy Rideau

    (Université Paris VII, Laboratoire de Physique Théorique et Mathématique)

Abstract

Recently, a Hamiltonian formalism was presented which treats the singular nature of Bateman Lagrangians describing quasi-linear integro-differential equations. This is in exchange for the pairing of a given system of equations with another system via Bateman’s Lagrangian prescription. One possible important consequence of this approach in the case of a system of ordinary differential equations is that a particular Bateman pair may form a completely integrable Hamiltonian system even though the original system is not one. It is the main purpose of this paper to exhibit concrete detailed examples of such systems.

Suggested Citation

  • Robert L. Anderson & Piotr W. Hebda & Guy Rideau, 1993. "Examples of Completely Integrable Bateman Pairs," Springer Books, in: N. H. Ibragimov & M. Torrisi & A. Valenti (ed.), Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, pages 23-33, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-2050-0_3
    DOI: 10.1007/978-94-011-2050-0_3
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