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Multiparametric solutions to the Gardner equation and the degenerate rational case
pierre gaillard
Keywords:Gardner equation, wronskians, rational solutions
Abstract:
      We construct solutions to the Gardner equation in terms of wronskians 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.