We now make the following substitutions, motivated by the decomposition of traveling-wave solutions (of the ordinary wave equation, to which this reduces when α α , h vanish) into left- and right-moving waves, so that we only consider a right-moving wave. Let ξ ξ = x − − c t , τ τ = ( α α h ) c t , y ( ξ ξ , τ τ ) = u ( x , t ) . Under this change of coordinates, the equation becomes