Rational solutions of order N to the KPI equation with multi-parameters and the explicit case of order 3 - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2022

Rational solutions of order N to the KPI equation with multi-parameters and the explicit case of order 3

P Gaillard
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Abstract

We present multiparametric rational solutions to the Kadomtsev-Petviashvili equation (KPI). These solutions of order N depend on 2N − 2 real parameters. Explicit expressions of the solutions at order 3 are given. They can be expressed 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. We study the patterns of their modulus in the (x,y) plane for different values of time t and parameters.
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Dates and versions

hal-03688578 , version 1 (05-06-2022)

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  • HAL Id : hal-03688578 , version 1

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P Gaillard. Rational solutions of order N to the KPI equation with multi-parameters and the explicit case of order 3. 2022. ⟨hal-03688578⟩
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