Isaac Scientific Publishing

New Horizons in Mathematical Physics

Families of Rational Solutions of Order 5 to the KPI Equation Depending on 8 Parameters

Download PDF (1121.2 KB) PP. 26 - 32 Pub. Date: June 23, 2017

DOI: 10.22606/nhmp.2017.11004


  • P. Gaillard*
    Université de Bourgogne, Institut de mathématiques de Bourgogne, 9 avenue Alain Savary BP 47870 21078 Dijon Cedex, France


In this paper, we go on with the study of rational solutions to the Kadomtsev-Petviashvili
equation (KPI). We construct here rational solutions of order 5 as a quotient of 2 polynomials of
degree 60 in
x, y and t depending on 8 parameters. The maximum modulus of these solutions at
order 5 is checked as equal to 2(2
N + 1)2 = 242. We study their modulus patterns in the plane
x, y) and their evolution according to time and parameters a1, a2, a3, a4, b1, b2, b3, b4. We get
triangle and ring structures as obtained in the case of the NLS equation.


Kadomtsev petviashvili equation, rogue waves, lumps


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