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Characterizing far from equilibrium states of the one-dimensional nonlinear Schr{ö}dinger equation
by Abhik Kumar Saha, Romain Dubessy
Submission summary
| Authors (as registered SciPost users): | Romain Dubessy |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2210.09812v2 (pdf) |
| Date submitted: | 2024-05-25 08:52 |
| Submitted by: | Dubessy, Romain |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We use the mathematical toolbox of the inverse scattering transform to study quantitatively the number of solitons in far from equilibrium one-dimensional systems described by the defocusing nonlinear Schr{\"o}dinger equation. We present a simple method to identify the discrete eigenvalues in the Lax spectrum and provide a extensive benchmark of its efficiency. Our method can be applied in principle to all physical systems described by the defocusing nonlinear Schr{\"o}dinger equation and allows to identify the solitons velocity distribution in numerical simulations and possibly experiments.
Current status:
Reports on this Submission
Strengths
1- The manuscript is based on a simple yet powerful idea
2- Well written and easy to follow
3- The proposed method is potentially useful for numerical simulations
4- As per the evidence provided the proposed method appears to work well for identifying dark and grey solitons
Weaknesses
1- Restrictive use cases - the proposed method is limited to homogeneous backgrounds where the inverse scattering theory applies
2- Not useful for experimental studies where usually only density information but not phase information is available
Report
This is a well-written manuscript about a new method to detect dark and grey solitons in numerical solutions of the nonlinear Schroedinger equation starting from a simple idea that is based on the powerful inverse scattering transform. Section 2 where the soliton indicator is introduced is very clear and easy to follow. The referencing of previous work appears adequate.
I was a bit confused by Sec. 3.1 where empirical thresholds $\epsilon_-$ and $\epsilon_+$ given by numerical values are introduced while no reference is made to the theoretically motivated threshold defined in Sec. 2, $\epsilon = \pi^2/(4L^2\sqrt{gn_0})$. As the argument in Sec. 2 appears to make perfect sense, why not use the numerical studies in Sec. 3 to validate it (or understand in which situations it may fail)?
While the proposed method appears to be potentially useful for numerical studies of generalized hydrodynamics, the introduction also references previous work where solitons had to be identified from experimental data (Ref. [46]). I'd like to encourage the authors to consider and comment on whether their approach could be extended to deal with missing information, i.e. specifically the situation where only density but no phase information is available.
Requested changes
1- Please add a discussion relating the empirical thresholds $\epsilon_-$ and $\epsilon_+$ to the theoretical threshold $\epsilon$ of Sec. 2. Moreover, it would be potentially more instructive and generally useful to give the thresholds in unit of $\epsilon$ rather than just as bare dimensionless numbers (which only make sense for particular chosen numerical parameters).
2- The blue solid line in Fig. 6a for eigenvalues identified by the threshold $\epsilon_+$ appears to zero for most bins. Does that mean that this threshold fails? Please discuss the implication, or correct the plot if this is just a mistake.
3- The same figure caption mentioned cyan lines corresponding to some some numerical factor multiplied to c. What is the signifcance of the particular factor? Why were these lines included in the plot? Please clarify!
Recommendation
Ask for minor revision