точные решения

Lie Symmetry Analysis and Some New Exact Solutions for a Variable Coefficient Modified Kortweg – De Vries Equation Arising in Arterial Mechanics

Authors: Abdel Latif M. S.

In this paper, a variable-coefficient modified Korteweg – de Vries equation is considered. By using the classical symmetry analysis method symmetries for this equation are obtained. Then, the generalized Jacobi elliptic function expansion method is used to solve the reduced ODE. Some new exact solutions for the considered PDE are obtained.

Exact Solutions of the Transonic Equations of Gas Dynamics

Authors: Kuznetsova E. O., Chernov I. A.

The review exact (described by algebraic functions) solutions of a transonic set of Karman–Falkovitch equations is given. Self-similar solutions and two classes of the polynomial-parametrical solutions associated with self-similar at indexes n = 2 and n = 3 are considered. Connection with local exposition of singularities of transonic flows is specified , in particular in Laval nozzles.