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Can one hear the full nonlinearity of a PDE from its small excitations?
by Maxim Olshanii, Danshyl Boodhoo
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Submission summary
| Authors (as registered SciPost users): | Danshyl Boodhoo · Maxim Olshanii |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2407.05215v2 (pdf) |
| Date accepted: | July 30, 2025 |
| Date submitted: | June 18, 2025, 4 a.m. |
| Submitted by: | Danshyl Boodhoo |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this article, we show how one can restore an unknown nonlinear partial differential equation of a sine-Gordon type from its linearization around an unknown stationary kink. The key idea is to regard the ground state of the linear problem as the translation-related Goldstone mode of the nonlinear PDE sought after.
Author comments upon resubmission
This resubmission addresses comments from reviewers.
List of changes
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Added a regularity condition on the nonlinearity $F(u)$
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Added a section on the relevance, or lack thereof, of the arbitrary constants A and B
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Added an example calculation for the method that reproduces the sine-Gordon equation for a given choice of A and B.
Published as SciPost Phys. Core 8, 055 (2025)
Reports on this Submission
Report
Thank you for the clear responses to the questions posed by both referees. Seeing these clarifications, I see that my comment regarding rotational invariance is not relevant to the problem being solved (or to a natural extensions in higher dimensions). The corrections made within the article address my questions directly while not detracting from the main conclusions of the article. I recommend the corrected version for publication.
Recommendation
Publish (meets expectations and criteria for this Journal)