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Can one hear the full nonlinearity of a PDE from its small excitations?
by Maxim Olshanii, Danshyl Boodhoo
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
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.
Current status:
Editorial decision:
For Journal SciPost Physics Core: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
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