From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters, the structure of the solutions and the case of fourth order

Abstract : We have already constructed solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants and wronskians of order 2N. These solutions have been called solutions of order N and they depend on 2N − 1 parameters. We construct here N-order rational solutions. We prove that they can be written as a quotient of 2 polynomials of degree 2N (N + 1) in x, y and t depending on 2N − 2 parameters. We explicitly construct the expressions of the rational solutions of order 4 depending on 6 real parameters and we study the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters a1, a2, a3, b1, b2, b3.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01525384
Contributeur : Pierre Gaillard <>
Soumis le : samedi 19 août 2017 - 09:44:32
Dernière modification le : lundi 9 octobre 2017 - 15:18:24

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halKPRAT2NSMMV1.pdf
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  • HAL Id : hal-01525384, version 2

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Pierre Gaillard. From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters, the structure of the solutions and the case of fourth order. 2017. 〈hal-01525384v2〉

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