N order solutions with multi-parameters to the Boussinesq and KP equations and the degenerate rational case - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2021

N order solutions with multi-parameters to the Boussinesq and KP equations and the degenerate rational case

Abstract

From elementary exponential functions which depend on several parameters, we construct multi-parametric solutions to the Boussinesq equation. When we perform a passage to the limit when one of these parameters goes to 0, we get rational solutions as a quotient of a polynomial of degree N (N + 1) − 2 in x and t, by a polynomial of degree N (N + 1) in x and t for each positive integer N depending on 3N parameters. We restrict ourself to give the explicit expressions of these rational solutions for N = 1 until N = 3 to shortened the paper. We easily deduce the corresponding explicit rational solutions to the Kadomtsev Petviashvili equation for the same orders from 1 to 3.
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Dates and versions

hal-03142778 , version 1 (16-02-2021)

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  • HAL Id : hal-03142778 , version 1

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Pierre Gaillard. N order solutions with multi-parameters to the Boussinesq and KP equations and the degenerate rational case. 2021. ⟨hal-03142778⟩
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