On one typical Einstein-Weyl equation: inverse spectral transform for theCauchy problem, longtime behaviour of the solutions and implicit solutions
Exactly Solvable and Integrable Systems
2025-04-03 v1
Abstract
In this paper, we study one typical Einstein-Weyl equation. It arises from Ferapontov and Kruglikov's investigation on the integrability of several dispersionless partial differential equations and the geometry of their formal linearizations. First, by using Manakov-Santini IST (inverse spectral transform) method, we investigate its Cauchy problem including the direct problem from the initial data, the time evolution of the scattering and spectral data, and the inverse problem. Second, based on the nonlinear RH (Riemann-Hilbert) dressing, the longtime behaviour of the solutions is constructed. In addition, some implicit solutions are presented.
Keywords
Cite
@article{arxiv.2504.01361,
title = {On one typical Einstein-Weyl equation: inverse spectral transform for theCauchy problem, longtime behaviour of the solutions and implicit solutions},
author = {Ge Yi and Zikai Chen and Kelei Tian and Ying Xu},
journal= {arXiv preprint arXiv:2504.01361},
year = {2025}
}