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A bilocal periodic problem for the Sturm-Liouville and Dirac operators and some applications to the theory of nonlinear dynamical systems. I

Abstract

Isospectral problems for operator-valued Sturm-Liouville and Dirac differential expressions are considered. Within the framework of the gradient method, one establishes the complete integrability of the Lax associated nonlinear Hamiltonian systems with a bilocal implectic pair of Noetherian operators on a manifold of integral operators.

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 794–800, June, 1990.

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Bogolyubov, N.N., Prikarpatskii, A.K. A bilocal periodic problem for the Sturm-Liouville and Dirac operators and some applications to the theory of nonlinear dynamical systems. I. Ukr Math J 42, 702–707 (1990). https://doi.org/10.1007/BF01058917

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Keywords

  • Dynamical System
  • Integral Operator
  • Hamiltonian System
  • Gradient Method
  • Dirac Operator