A method of constructing canonical equations for quantum liquids is proposed. For superfluid 4He the forms of the Hamiltonian equations of hydrodynamics and conservation laws are obtained. The kinetic terms in the equations of hydrodynamics are written out. The set of equations obtained is valid up to the λ point. For anisotropic quantum liquid 3He-A canonical equations both for spin and orbital hydrodynamics are found with the spin and orbital moments taken into account. The forms of the laws of the conservation of momentum, angular momentum, mass, and energy are obtained. The kinetic terms in the equations of hydrodynamics are considered, and both the dissipative and reactive coefficients are classified. A transfer equation for the order parameter near the A transition point is proposed with the dissipative term taken into account.
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Khalatnikov, I.M., Lebedev, V.V. Canonical equations of hydrodynamics of quantum liquids. J Low Temp Phys 32, 789–801 (1978). https://doi.org/10.1007/BF00056658
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DOI: https://doi.org/10.1007/BF00056658