TY - JOUR
T1 - Rational Solutions to the KdV Equation in Terms of Particular Polynomials
AU - Gaillard , Pierre
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 615
EP - 627
PY - 2023
DA - 2023/08
SN - 4
DO - http://doi.org/10.12150/jnma.2022.615
UR - https://global-sci.org/intro/article_detail/jnma/21901.html
KW - Polynomial, Bilinear differential operator, Rational solution.
AB - <p style="text-align: justify;">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.</p>