Explicit classical solutions and comments on Higher-Derivative Klein-Gordon equation in (1+1)-D

Abstract

We present a simple and general method to solve higher-power D'Alembert equation in (1+1) dimensions for a set of completely general initial conditions. Explicit solutions are written down for the cases of $\Box^{2}$ and $\Box^{3}$ and the singularity structure is manifest through the derivative terms of some of the initial-condition functions. The explicit solutions found out may be useful if one wishes to device external sources which may suppress the non-physical modes introduced by the higher derivatives.