Rational solutions to the KdV equation from Riemann theta functions

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.

کلیدواژه ها:

KdV equation ، Riemann theta functions ، wronskians ، Fredholm determinants