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A differential-algebraic approach to studying the Lax type integrability ofthe generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. Theapproach is also applied to studying the Lax type integrability of the wellknown Korteweg-de Vries dynamical system.

Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations