On the complete integrability and linearization of a Burgers– Korteweg–de Vries-type nonlinear equation
- 33 Downloads
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.
KeywordsSoliton Nonlinear Dynamical System Independent Invariant Polynomial Vector Field Infinite Hierarchy
Unable to display preview. Download preview PDF.
- 1.O. Hentosh, M. Prytula, and A. Prykarpats’kyi, Differential Geometric and Li-Algebraic Fundamentals of the Investigation of Integrable Nonlinear Dynamical Systems on Functional Manifolds [in Ukrainian], Lviv University, Lviv (2006).Google Scholar
- 2.P. I. Holod and A. I. Klimyk, Mathematical Fundamentals of the Theory of Symmetries [in Ukrainian], Naukova Dumka, Kiev (1992).Google Scholar
- 3.A. M. Samoilenko and Ya. A. Prykarpats’kyi, Algebraic-Analytical Aspects of Completely Integrable Dynamical Systems and Their Perturbations [in Ukrainian], Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev (2002).Google Scholar