Symmetries and exact solutions of some classes of nonlinear difference equations (Q2739118)

The authors extend techniques of Lie groups for solving differential equations to difference equations \(u(x+\omega)=\sum_{i=1}^na_iu^i(x)\), where \(a_i\) satisfy \(a_n=b^{n-1}=1\), \(a_{n-i}=C_n^ib^ia_n\), \(i=1,2,\cdots,n-1\), \(\omega\) and \(b\) are real numbers except zero. The invariant transformations of three classes of nonlinear difference equations are given. The exact solutions of those difference equations can be obtained by using the invariant transformation.