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

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Abstract

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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Link: https://cloud.u-bourgogne.fr/index.php/apps/files/?dir=/ &fileid=21800026 Folder: KP NODY Password: https://cloud.u-bourgogne.fr/index.php/s/rASsMndjQmXFPF4

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  1. Université de Bourgogne Franche Comté, Institut de mathématiques de Bourgogne, 9 avenue Alain Savary BP 47870, 21078, Dijon Cedex, France

    Pierre Gaillard

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  1. Pierre Gaillard
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Correspondence to Pierre Gaillard.

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This article is part of the section “Computational Approaches” edited by Siddhartha Mishra.

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Gaillard, P. Families of solutions to the KPI equation given by an extended Darboux transformation. Partial Differ. Equ. Appl. 3, 80 (2022). https://doi.org/10.1007/s42985-022-00212-0

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