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Preprints, Working Papers, ... Year : 2018

Families of solutions to the KPI equation and the structure of their rational representations of order N

Abstract

We construct solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants. We deduce solutions written as a quotient of wronskians of order 2N. These solutions called solutions of order N depend on 2N − 1 parameters. They can also be written as a quotient of two polynomials of degree 2N (N + 1) in x, y and t depending on 2N − 2 parameters. The maximum of the modulus of these solutions at order N is equal to 2(2N + 1) 2. We explicitly construct the expressions until the order 6 and we study the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters.
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Dates and versions

hal-01865763 , version 1 (01-09-2018)

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  • HAL Id : hal-01865763 , version 1

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Pierre Gaillard. Families of solutions to the KPI equation and the structure of their rational representations of order N. 2018. ⟨hal-01865763⟩
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