Rational solutions to the KdV equation from Riemann theta functions

محورهای موضوعی : Journal of Theoretical and Applied Physics

Pierre Gaillard ¹ (Institute of Mathematics, University of Bourgogne, Dijon, France.)

تاریخ دریافت : 1401/08/11 تاریخ پذیرش : 1401/12/19 تاریخ انتشار : 1402/04/10

کلید واژه: wronskians, KdV equation, Fredholm determinants, Riemann theta functions,

چکیده مقاله :

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.