| Abstract: | We propose a constructive method for the construction of exact solutions of nonlinear partial differential equations. The
method is based on the investigation of a fixed nonlinear partial differential equation (system of partial differential equations)
together with an additional condition in the form of a linear ordinary differential equation of higher order. By using this
method, we obtain new solutions for nonlinear generalizations of the Fisher equation and for some nonlinear evolution systems
that describe real processes in physics, biology, and chemistry.
To the blessed memory of V. I. Fushchich
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49,
No. 6, pp. 814–827, June, 1997. |
