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arXiv · 2606.08321

Inverse scattering for the focusing nonlinear Schr\"odinger equation with elliptic background and full soliton gas

Tamara Grava·Robert Jenkins·Xiaofan Zhang·Zechuan Zhang
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Abstract

In this manuscript we develop the direct and inverse scattering problem for the cubic focusing nonlinear Schr\"odinger equation and for initial data that are asymptotic to an elliptic travelling wave with distinct phase at $\pm \infty$. We consider the case in which the spectral bands intersect the real axis. We then show that this class of initial data has non zero intersection with the full soliton gas initial data.

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Tamara Grava, Robert Jenkins, Xiaofan Zhang, Zechuan Zhang. 2026-06-06. Inverse scattering for the focusing nonlinear Schr\"odinger equation with elliptic background and full soliton gas. https://arxiv.org/abs/2606.08321

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