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Preprints, Working Papers, ... Year : 2022

Solutions to the Gardner equation with multiparameters and the rational case

Abstract

We construct solutions to the Gardner equation in terms of trigonometric and hyperbolic functions, depending on several real parameters. Using a passage to the limit when one of these parameters goes to 0, we get, for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2N parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 3. We easily deduce solutions to the mKdV equation in terms of wronskians as well as rational solutions depending on 2N real parameters.
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Dates and versions

hal-03540008 , version 1 (22-01-2022)

Identifiers

  • HAL Id : hal-03540008 , version 1

Cite

Pierre Gaillard. Solutions to the Gardner equation with multiparameters and the rational case. 2022. ⟨hal-03540008⟩
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