Abstract:
A nonlinear differential equation of the second order of the Riccati hierarchy is considered. The concept of a generalized solution for such an equation cannot be introduced in the classical theory of generalized functions because the product of generalized functions is not defined. To introduce the concept of a generalized solution, an approach is considered in which the construction of a generalized solution of the second equation of the Riccati hierarchy is carried out using approximation by solutions of the Cauchy problem with complex initial conditions. The total number of generalized solutions depends on the initial conditions of the Cauchy problem, and their form depends on the location of the poles of the approximating solutions.
Keywords:generalized function, generalized solution of a nonlinear differential equation, Painleve property.
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