Abstract
Solutions of differential-difference Korteweg-de Vries (KdV), modified KdV and generalized KdV equations are given in terms of theta functions. The dispersion relation is given in elegant, compact forms and the solutions consist of a sequence of solitions. A fully discrete or partial difference KdV equation is also treated. A new identity in theta function enables the elliptic function solution to be rewritten as a sum of solitons.
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