TY - EJOUR
AU - Gaillard, Pierre
PY - 2023
DA - November
TI - Rational solutions to the KdV equation from Riemann theta functions
T2 - Journal of Theoretical and Applied Physics
VL - 17
L1 - https://oiccpress.com/journal-of-theoretical-and-applied-physics/article/rational-solutions-to-the-kdv-equation-from-riemann-theta-functions/
DO - 10.57647/J.JTAP.2023.1703.27
N2 - 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.
IS - 3
PB - OICC Press
KW - Wronskians, Fredholm determinants, KdV equation, Riemann theta functions 
EN -