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

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.
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Submitted on : Tuesday, September 25, 2018 - 12:09:16 PM
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P. Gaillard. Multiparametric Families of Solutions of the Kadomtsev–Petviashvili-I Equation, the Structure of Their Rational Representations, and Multi-Rogue Waves. Theor.Math.Phys., 2018, 196 (2), pp.1174-1199. ⟨10.1134/S0040577918080068⟩. ⟨hal-01880923⟩

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