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Theoretical and Mathematical Physics

, Volume 196, Issue 2, pp 1174–1199 | Cite as

Multiparametric Families of Solutions of the Kadomtsev–Petviashvili-I Equation, the Structure of Their Rational Representations, and Multi-Rogue Waves

  • P. GaillardEmail author
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Abstract

We construct solutions of the Kadomtsev–Petviashvili-I equation 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 up to the order six and study the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters.

Keywords

Kadomtsev–Petviashvili equation Fredholm determinant Wronskian lump rogue wave 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Université de Bourgogne, Institut de mathématiques de BourgogneFaculté des Sciences MirandeDijonFrance

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