Figure 7

Comparison of solutions from the leading order terms [Eqs. (d5)–(d8)] with the corresponding numerical solutions at the critical point \(g=1\): \(n_{c}\) [(a)–(b)], \(\epsilon_{s}\) [(c)–(d)], Δx [(e)–(f)], and Δp [(g)–(h)]. The dashed lines plot their leading order terms with analytical solutions, and the solid lines plot the corresponding numerical solutions