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Preprints, Working Papers, ... Year : 2022

Other patterns for the first and second order rational solutions to the KPI equation

Abstract

We present rational solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of polynomials in x, y and t depending on several real parameters. We get an infinite hierarchy of rational solutions written as a quotient of a polynomial of degree 2N (N + 1) − 2 in x, y and t by a polynomial of degree 2N (N + 1) in x, y and t, depending on 2N − 2 real parameters for each positive integer N. We construct explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the (x, y) plane for different values of time t and parameters. In particular, in the study of these solutions, we see the appearance not yet observed of three pairs of two peaks in the case of order 2.
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Dates and versions

hal-03576395 , version 1 (16-02-2022)

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  • HAL Id : hal-03576395 , version 1

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Pierre Gaillard. Other patterns for the first and second order rational solutions to the KPI equation. 2022. ⟨hal-03576395⟩
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