Abstract.The problem of identifying whether a given nonlinear partial differential equation admits a linear integrable system is studied here. It is shown that the fundamental equations of surface theory can be used to reproduce the compatibility conditions obtained from a linear system in matrix form corresponding to a number of different Lie algebras. It is also shown that the system of equations which has been obtained from the linear matrix problem can also be derived from a set of differential forms.

Received: February 11, 2008

AMS Subject Classification: 53Z05, 53A10, 53B50, 53C217

Key Words and Phrases: partial differential equation, integrable systems, Gaussian curvature

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 43
Issue: 3