Can one hear the full nonlinearity of a PDE from its small excitations?

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.

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Publication Details

Journal
SciPost Physics Core
Published
2025-08-25
DOI
https://doi.org/10.21468/scipostphyscore.8.3.055
Primary Topic
Nonlinear Photonic Systems
Type
article
Field-Weighted Citation Impact
0.00

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article

Can one hear the full nonlinearity of a PDE from its small excitations?

Maxim Olshanii, Danshyl Boodhoo
SciPost Physics Core
Nonlinear Photonic Systems
article

Can one hear the full nonlinearity of a PDE from its small excitations?

Maxim Olshanii, Danshyl Boodhoo
article en

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.

SciPost Physics CoreVol. 8(3)
University of Massachusetts Boston (US)
National Science Foundation
Openalex Percentile: Top 83%
Nonlinear Photonic Systems
DOIOpen Access PDFOpenAlex
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Can one hear the full nonlinearity of a PDE from its small excitations? — Maxim Olshanii, Danshyl Boodhoo · SciPost Physics Core (2025) | TGRS Research Map | TGRS