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Elements of Differential Calculus for Tensor Fields
The Theory of Hamiltonian and BiHamiltonian Systems
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1)-dimensional adjoint AKNS arbitrary bi-Hamiltonian chain bi-Hamiltonian formulation canonical Casimir commutator compatible conserved quantities constraint construct cosymmetries covector defined denote differential operator dynamical system eigenfunctions equivalent evolution equations Example field systems finite dimensional given Hamiltonian formulation Hamiltonian system Hamiltonian vector field Hence hereditary algebra implectic operator infinite integrable inverse isospectral Jacobi identity KdV equation KdV hierarchy Lagrangian lattice Lax equations Lax operators Lax pair Lax representation Lemma Lie algebra Lie derivative linear manifold master symmetries matrix Miura map MKdV modified multi-Hamiltonian N-soliton Newton representation Nijenhuis coordinates nonisospectral nonlinear obtain operator 9 Ostrogradsky representation parameter phase space Poisson bracket Poisson operator Poisson structure Poisson tensor Proof quadratic recursion operator respect restricted flows satisfies scalar fields soliton solutions spectral problem stationary flow subalgebra subspace symplectic takes the form tensor field tensor invariants Theorem theory transformation zero-curvature