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<p>On the basis of the gradient holonomic method of investigation of the integrability of nonlinear dynamical systems on functional manifolds, we establish the exact Lax-type linearization of the nonlinear Calogero-Degasperis dynamical system, its bi-Hamiltonian property, and construct an infinite hierarchy of functional independent invariants. As a result, we obtain a compatible pair of related Poisson structures.</p>

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ON THE COMPLETE INTEGRABILITY AND LINEARIZATION OF THE NONLINEAR CALOGERO–DEGASPERIS EQUATION

  • 期刊论文

  • 发表日期：

    2025年7月31日

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  • Mykola Prytula,
  • Yaryna Kokovska

摘要

On the basis of the gradient holonomic method of investigation of the integrability of nonlinear dynamical systems on functional manifolds, we establish the exact Lax-type linearization of the nonlinear Calogero-Degasperis dynamical system, its bi-Hamiltonian property, and construct an infinite hierarchy of functional independent invariants. As a result, we obtain a compatible pair of related Poisson structures.