Rational Solutions to the KdV Equation in Terms of Particular Polynomials (Journal of Nonlinear Modeling and Analysis, 2024)
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 tothe KdV equation, and we can construct explicit solutions very easily. In thefollowing, we present some solutions until order 10.
Keywords: Polynomial; Bilinear differential operator; Rational solution.