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

Author

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  • Pierre Gaillard

    (Université de Bourgogne Franche Comté, Institut de mathématiques de Bourgogne)

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.

Suggested Citation

  • Pierre Gaillard, 2022. "Families of solutions to the KPI equation given by an extended Darboux transformation," Partial Differential Equations and Applications, Springer, vol. 3(6), pages 1-14, December.
    • Handle: RePEc:spr:pardea:v:3:y:2022:i:6:d:10.1007_s42985-022-00212-0
    DOI: 10.1007/s42985-022-00212-0
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