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Article Dans Une Revue Journal of Applied Analysis and Computation Année : 2021

Multiparametric solutions to the Gardner equation and the degenerate rational case

Résumé

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.

Dates et versions

hal-03466924 , version 1 (06-12-2021)

Identifiants

Citer

Pierre Gaillard. Multiparametric solutions to the Gardner equation and the degenerate rational case. Journal of Applied Analysis and Computation, 2021, 11 (4), pp.2102-2113. ⟨10.11948/20200332⟩. ⟨hal-03466924⟩
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