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Preprints, Working Papers, ... Year : 2016

Fredholm representations of solutions to the KPI equation, their wronkian versions and rogue waves

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. When one of these parameters tends to zero, we obtain N order rational solutions expressed as a quotient of two polynomials of degree 2N (N + 1) in x, y and t depending on 2N − 2 parameters. So we get with this method an infinite hierarchy of solutions to the KPI equation.
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Dates and versions

hal-01330610 , version 1 (13-06-2016)

Identifiers

  • HAL Id : hal-01330610 , version 1

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Pierre Gaillard. Fredholm representations of solutions to the KPI equation, their wronkian versions and rogue waves. 2016. ⟨hal-01330610⟩
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