On integrable by quadratures generalized Riccati-Abel equations: Differential-geometric and Lie-algebraic analysis (Q1573848)

The paper addresses the problem of integrability by quadratures of a generalized Riccati-Abel equation. First, the Cauchy problem for the given equation is reduced to an equivalent system of nonlinear partial differential equations with the Cauchy-Goursat initial data. Then the Lax type integrability of the reduced problem is proved. This establishes the integrability by quadratures of a generalized Riccati-Abel equation due to the equivalence of the obtained integrability condition to the integrable Liouville equation.