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Rational Solutions to the KdV Equation in Terms of Particular Polynomials
  
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KeyWord:Polynomial; Bilinear differential operator; Rational solution
Author NameAffiliation
Pierre Gaillard Institut de Math\'ematiques, Universit\'e de Bourgogne-Franche Comt\'e, Dijon, 21000, France 
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Abstract:
      Here, we construct rational solutions to the KdV equation by particular polynomials. We get the solutions in terms of determinants of the order $n$ for any positive integer $n$, and we call these solutions, solutions of the order $n$. Therefore, we obtain a very efficient method to get rational solutions to the KdV equation, and we can construct explicit solutions very easily. In the following, we present some solutions until order $10$.