2024/04/06 by Gaillard, Pierre
#Fredholm determinants #KdV equation #Riemann theta functions #Wronskians
paper · doi:10.57647/j.jtap.2023.1704.27
Rational solutions to the KdV are constructed from the finite gap solutions of the KdV equation given in terms of abelian functions. For this we use a previous result giving the connection between Riemann theta functions and Fredholm determinants and also wronskians. By choosing the parameters of these solutions according to a number intended to move towards zero, we obtain rational solutions when this number tends towards zero. So, we construct a hierarchy of rational solutions depending on multi real parameters and we give explicitly expressions for the first orders.