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Journal Articles New Horizons in Mathematical Physics Year : 2017

Families of rational solutions of order 5 to the KPI equation depending on 8 parameters

Abstract

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(2N + 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.
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Dates and versions

hal-01598396 , version 1 (29-09-2017)

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Pierre Gaillard. Families of rational solutions of order 5 to the KPI equation depending on 8 parameters. New Horizons in Mathematical Physics, 2017, 1 (1), pp.26-32. ⟨10.22606/nhmp.2017.11004⟩. ⟨hal-01598396⟩
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