SYMMETRY AND SOME EXACT-SOLUTIONS OF NONLINEAR POLYWAVE EQUATIONS

We have studied the maximal symmetry group admitted by the non-linear polywave equation square(l)u = F(u). In particular, we establish that the equation in question admits the conformal group C(1, n) if and onl y if F(u) = lambda e(u), n + 1 = 2l or F(u) = lambda u((n+1+2l)/(n+1-2 l)) n + 1 not equal 2l. Symmetry reduction for the biwave equation squ are(2)u = lambda u(-3) is carried out and some exact solutions are obt ained.