| Citation: |
Pierre Gaillard. MULTIPARAMETRIC SOLUTIONS TO THE GARDNER EQUATION AND THE DEGENERATE RATIONAL CASE[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 2102-2113. doi: 10.11948/20200332
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MULTIPARAMETRIC SOLUTIONS TO THE GARDNER EQUATION AND THE DEGENERATE RATIONAL CASE
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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 para-meters goes to zhongwenzy, we get, for each positive integer $N$, rational solutions as a quotient of polynomials in $x$ and $t$ depending on 2$N$ 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 2$N$ real parameters.
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Keywords:
- Gardner equation /
- Wronskians /
- rational solutions
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References
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Pierre Gaillard. MULTIPARAMETRIC SOLUTIONS TO THE GARDNER EQUATION AND THE DEGENERATE RATIONAL CASE[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 2102-2113. doi: 10.11948/20200332
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