Journal of Mathematical Sciences

, Volume 167, Issue 1, pp 112–117 | Cite as

On the complete integrability and linearization of a Burgers– Korteweg–de Vries-type nonlinear equation

  • M. M. Prytula
  • A. K. Prykarpats’kyi
  • M. I. Vovk

In this work, on the basis of the Bogolyubov–Prykarpats’kyi gradient–holonomic algorithm for the investigation of the integrability of nonlinear dynamical systems on functional manifolds, the exact linearization of a Burgers–Korteweg–de Vries-type nonlinear dynamical system is established. As a result, we describe the linear structure of the space of solutions and show its relation to the convexity of certain functional subsets. The bi-Hamiltonian property of the Burgers–Korteweg–de Vries dynamical system is also established, and the infinite hierarchy of functionally independent invariants is constructed.


Soliton Nonlinear Dynamical System Independent Invariant Polynomial Vector Field Infinite Hierarchy 
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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • M. M. Prytula
    • 1
  • A. K. Prykarpats’kyi
    • 2
    • 3
  • M. I. Vovk
    • 4
  1. 1.Franko Lviv National UniversityLvivUkraine
  2. 2.Franko Drohobych State Pedagogic UniversityDrohobychUkraine
  3. 3.AGH University of Science and TechnologyCracowPoland
  4. 4.“L’vivs’ka Politekhnika” National UniversityLvivUkraine

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