Geometric approach for finding exact solutions to nonlinear partial differential equations

Stimulated by contact geometry, we establish a method for finding exact solutions to nonlinear partial differential equations by solving nonlinear partial differential equations with lower order. Within the present theoretical framework, some equations arising from physics, mechanics, engineering and geometry (such as the governing equations of vibrations of a nonlinear string; propagation of sound waves in a compressible fluid; surfaces with negative Gaussian curvature and so on) are investigated. (C) 1998 Published by Elsevier Science B.V.