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arXiv · 2606.14986

Modulation theory for lumps and interactions between lumps and a mean field in the Kadomtsev-Petviashvili equation

Gino Biondini·Sergey Dyachenko·Mark A. Hoefer·Nicholas J. Ossi
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Abstract

A (2+1)-dimensional hyperbolic system of four quasi-linear partial differential equations is derived that describes the modulations of lump solutions of the Kadomtsev-Petviashvili I (KPI) equation in the presence of a mean field. The system is then shown to satisfy the necessary conditions for integrability of hydrodynamic chains. Moreover, a suitable reduction of the resulting modulation system is applied to study the interactions between lumps and a rarefaction wave for the mean field. Precise conditions are derived that describe how the lump parameters change as a result of the interaction, and which in particular determine whether the lump is transmitted through or trapped inside the rarefaction wave. The theoretical predictions are compared to direct numerical simulations of the KPI equation, showing excellent agreement.

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Gino Biondini, Sergey Dyachenko, Mark A. Hoefer, Nicholas J. Ossi. 2026-06-12. Modulation theory for lumps and interactions between lumps and a mean field in the Kadomtsev-Petviashvili equation. https://arxiv.org/abs/2606.14986

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