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Pré-Publication, Document De Travail Année : 2024

One degree of summation's rational solutions to the KPI equation

Résumé

In this paper, we construct solutions to the Kadomtsev-Petviashvili equation (KPI) by using a Darboux transformation with particular genera-ting functions limited to one degree of summation. With this choice, we get rational solutions expressed in terms of a wronskian of order N depending on N(D+5) real parameters. In this case, we construct explicitly multi-parametric rational solutions to the KPI equation and we study the patterns of their modulus in the plane $(x,y)$ and their evolution according to time and parameters.
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hal-04535254 , version 1 (06-04-2024)

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  • HAL Id : hal-04535254 , version 1

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Pierre Gaillard. One degree of summation's rational solutions to the KPI equation. 2024. ⟨hal-04535254⟩
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