Reductions and Exact Solutions of Nonlinear Elliptic Systems of a Special Form

详细

We study a nonlinear system of two elliptic differential equations with nonlinearities depending on a product of powers of the unknown functions. Sufficient conditions for the system to be reducible to a single equation are obtained. Some cases are singled out for which we find classes of exact solutions expressed via elementary and harmonic functions and solutions of the Liouville equation.