@article{Gaillard_2023, title={Rational solutions to the KdV equation from Riemann theta functions}, volume={17}, url={https://oiccpress.com/journal-of-theoretical-and-applied-physics/article/rational-solutions-to-the-kdv-equation-from-riemann-theta-functions/}, DOI={10.57647/J.JTAP.2023.1703.27}, abstractNote={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.}, number={3}, journal={Journal of Theoretical and Applied Physics}, publisher={OICC Press}, author={Gaillard, Pierre}, year={2023}, month={Nov.}, keywords={Fredholm determinants, KdV equation, Riemann theta functions, Wronskians} }