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Article Dans Une Revue SN Partial Differential Equations and Applications Année : 2022

Families of solutions to the KPI equation given by an extended Darboux transformation

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-03907917 , version 1 (20-12-2022)

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Pierre Gaillard. Families of solutions to the KPI equation given by an extended Darboux transformation. SN Partial Differential Equations and Applications, 2022, 3 (6), pp.80. ⟨10.1007/s42985-022-00212-0⟩. ⟨hal-03907917⟩
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