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Elements of the theory of integrable systems
Slow perturbations of fieldtheoretic Hamiltonian systems
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abelian action variables action-angle variables analogue arbitrary asymptotic averaged system averaging method canonical coefficients commutative representation commuting flows compatibility completely integrable condition conservation laws const coordinates defined density diagonal metric differential differential-geometric Dokl Dubrovin equa equivalent evolutionary systems example fields finite finite-dimensional finite-gap fluid following formula functions geometry group G Hamilton-Lie group Hamiltonian formalism Hamiltonian SHT Hamiltonian system Hence Hopf algebra hydrodynamic type integrable system invariant manifolds invariant tori Jacobi identity KdV equation KdV hierarchy Korteweg-de Vries lattice Lemma Let us consider level surface Lie algebra Lie group linear matrix neighbourhood non-degenerate non-linear Novikov obtain one-dimensional operator parameters periodic perturbed phase space Phys Poisson brackets polynomial previous lecture problem Proof prove quantized quantum groups r2n+i Riemann surface Russian Math semi-Hamiltonian soliton spectral curve structure symmetry symplectic system of hydrodynamic target space tensor theorem tonian torus universal enveloping algebra vector vector-field Yang-Baxter equation