## Abstract

We show the relationship between the strongly non-linear limit (also termed the dispersionless or the Whitham limit) of the macroscopic fluctuation theory of certain statistical models and the inverse scattering method. We show that in the strongly non-linear limit the inverse scattering problem can be solved using the steepest descent method of the associated Riemann-Hilbert problem. The importance of establishing this connection, is that the equations in the strongly non-linear limit can often be solved exactly by simple means, the connection then provides a limit in which one can solve the inverse scattering problem, thus aiding potentially the exact solution of a particular large deviation problem.

Original language | American English |
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Article number | 035201 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 57 |

Issue number | 3 |

DOIs | |

State | Published - 19 Jan 2024 |

### Bibliographical note

Publisher Copyright:© 2024 The Author(s). Published by IOP Publishing Ltd

## Keywords

- Riemann-Hilbert problem
- invese scattering
- large deviations
- macroscopic fluctuation theory