Abstract
Symmetries of hydrodynamic equations with complex nonlinear terms and strong coupling are studied. Lie symmetry analysis of nonlinear Euler, Navier–Stokes and magnetohydrodynamic equations is presented using Lie group of transformations. The similarity reductions and exact solutions generated from the symmetry transformations are provided. Conservation laws of the equations are well constructed. The analytical method of the hydrodynamic equations is developed, which enriches the quantitative calculation results and realizes the scientific description of the hydrodynamic systems.
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