then the potential function V ( f ) has local maximum at f = 0 ; there is a solution in which f ( X ) starts at this point at 'virtual time' − − ∞ ∞ , eventually slides down to the local minimum, then back up the other side, reaching an equal height, and then reverses direction, ending up at the local maximum again at time ∞ ∞ . In other words, f ( X ) approaches 0 as X → → − − ∞ ∞ . This is the characteristic shape of the solitary wave solution.