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Gaillard, Pierre. (1402). Rational solutions to the KdV equation from Riemann theta functions. , 17(3), -. doi: 10.57647/J.JTAP.2023.1703.27
Pierre Gaillard. "Rational solutions to the KdV equation from Riemann theta functions". , 17, 3, 1402, -. doi: 10.57647/J.JTAP.2023.1703.27
Gaillard, Pierre. (1402). 'Rational solutions to the KdV equation from Riemann theta functions', , 17(3), pp. -. doi: 10.57647/J.JTAP.2023.1703.27
Gaillard, Pierre. Rational solutions to the KdV equation from Riemann theta functions. , 1402; 17(3): -. doi: 10.57647/J.JTAP.2023.1703.27

Rational solutions to the KdV equation from Riemann theta functions

Journal of Theoretical and Applied Physics
مقاله 2، دوره 17، شماره 3، مهر و آبان 2023  XML اصل مقاله (1.39 M)
نوع مقاله: Scientific Research Manuscript
شناسه دیجیتال (DOI): 10.57647/J.JTAP.2023.1703.27
نویسنده
Pierre Gaillard email
Institute of Mathematics, University of Bourgogne, Dijon, France.
چکیده
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.
کلیدواژه‌ها
KdV equation؛ Riemann theta functions؛ Wronskians؛ Fredholm determinants
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