lorenzifrancesco/npse-collapse

Where does the NPSE collapse?

We compute the chemical potential of the solitonic solution using

for various values of $\gamma$. Then, we can invert the implicit relation

and find the soliton shape.

The main conclusion here is that the collapse of the NPSE is not explicitly related to the vanishing of the transverse width

$$ \sigma^2 = \sqrt{1-2\gamma|f|^2} $$

since the maximum value of the axial wavefunction $(|f|^2)_{\mathrm{max}} \approx 0.46$ gives a width of $\sigma^2 \approx 0.62$ at the critical strength of $\gamma_c = 0.67$.