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Self-adjoint commuting differential operators of rank 2 and their deformations given by soliton equations. (English. Russian original) Zbl 1318.37014
Math. Notes 97, No. 3, 333-340 (2015); translation from Mat. Zametki 97, No. 3, 350-358 (2015).
Summary: Deformations of commutative rings of self-adjoint ordinary differential operators of rank 2 given by soliton equations are studied.
MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
47E05 General theory of ordinary differential operators
16S32 Rings of differential operators (associative algebraic aspects)
35Q53 KdV equations (Korteweg-de Vries equations)
16S80 Deformations of associative rings
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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