Can one hear the full nonlinearity of a PDE from its small excitations?
Analysis of PDEs
2025-08-27 v2 Quantum Gases
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2407.05215,
title = {Can one hear the full nonlinearity of a PDE from its small excitations?},
author = {Maxim Olshanii and Danshyl Boodhoo},
journal= {arXiv preprint arXiv:2407.05215},
year = {2025}
}