Affiliation:
1. Matrosov Institute for System Dynamics and Control Theory, Siberian Branch,
Russian Academy of Sciences
Abstract
Equations and systems of elliptic type with power-law nonlinearities are considered.Such equations are found in modeling distributed robotic formations, as well as in chemical kinetics,biology, astrophysics, and many other fields. The problem of constructing multidimensionalexact solutions is studied. It is proposed to use a special type of ansatz that reduces the problemto solving systems of algebraic equations. A number of multiparameter families of new exactmultidimensional solutions (both radially symmetric and anisotropic) represented by explicitformulas are obtained. Examples are given to illustrate the exact solutions found.
Publisher
The Russian Academy of Sciences