Abstract
This work obtains the stationary solutions of the non-linear Klein-Gordon equations in 1 + 1 dimensions. The technique that is used to carry out the analysis is the Lie symmetry approach. There are five types of non-linearity that are studied in this work. In each case, the analysis yields non-trivial stationary solutions; it is the first time that this has been seen. (C) 2010 Elsevier Ltd. All rights reserved.