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Pré-Publication, Document De Travail Année : 2023

An extended Darboux transformation to get families of solutions to the KPI equation

Résumé

By means of a Darboux transform with particular generating function solutions to the Kadomtsev-Petviashvili equation (KPI) are constructed. We give a method that provides different types of solutions in terms of particular determinants of order N. For any order, these solutions depend of the degree of summation and the degree of derivation of the generating functions. We study the patterns of their modulus in the plane (x, y) and their evolution according time and parameters.
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Dates et versions

hal-04014108 , version 1 (03-03-2023)

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  • HAL Id : hal-04014108 , version 1

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Pierre Gaillard. An extended Darboux transformation to get families of solutions to the KPI equation. 2023. ⟨hal-04014108⟩
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