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