General Symmetry Algebra Structure of the Exotic System ux = (vxx)(2)

摘要

In a recent paper Anderson, Kamran, and Olver obtained the first and second order Lie-Backlund symmetry algebra for the system u(sub x) = (v(sub xx))sup 2, leading to the exceptional Lie algebra G(sub 2). Here the authors obtain the structure of the general Lie-Backlund symmetry algebra. Moreover the Lie algebra G(sub 2) is obtained as ordinary symmetry algebra of the associated first order system. The general symmetry algebra for u(sub x) = f(u,v,v(sub x),...,) is established too.