Appendix 1—figure 2. Solutions to Equation 52 for $g=1$, $w=-1.8$, $\gamma =0$, $\mathrm{\Delta }x=0$.

Then, keeping u₀ fixed, we can repeat a similar procedure to find $\mathrm{\Delta }x$ for different values of γ. Also in this case, the solution either diverges or oscillates, apart from a single value $\mathrm{\Delta }{x}^{*}$, for which the solution has the desired shape (see Appendix 1—figure 3). This eliminates the arbitrariness in the choice of $\mathrm{\Delta }x$ since it imposes, for given $g$ and $w$, a relation $\mathrm{\Delta }x=\mathrm{\Delta }{x}^{*}(\gamma )$.