Conservation laws for the Korteweg-de Vries equation and the theory of partitions |
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| Institution: | 1. National Advanced School of Engineering, University of Yaounde I, P.O. Box 8390, Cameroon;2. Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Cameroon;3. Centre d’Excellence en Technologies de l’Information et de la Communication (CETIC), University of Yaounde I, P.O. Box 812, Yaounde, Cameroon;4. The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera, Trieste 11-I-34151, Italy |
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| Abstract: | We show how the terms appearing in the expressions for the densities and the fluxes for the Korteweg-de Vries equation may be found by combinatorial methods. Our basic device consists in associating partitions and their Ferrers graphs to the first density and to the first flux, and then in proceeding inductively following very simple rules. Furthermore, we use unrestricted partitions and a recurrence relation to specify every term of every integral power of the Sturm-Liouville (or one-dimensional Schrödinger) operator. |
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