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arXiv · 2407.05215

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

Maxim Olshanii·Danshyl Boodhoo
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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.

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Maxim Olshanii, Danshyl Boodhoo. 2024-07-07. Can one hear the full nonlinearity of a PDE from its small excitations?. https://doi.org/10.21468/scipostphyscore.8.3.055

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