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Abstract
The direct employment of the T-function defined as a limiting transformation of the Riemann theta function leading to a system of algebraic dispersion equations, yields solutions of some nonlinear partial differential equations in the form of solitons on a background of quasi-periodic waves. Pure solitons and pure quasi-periodic solutions appear as particular cases. The method is illustrated by the example of the KdV equation and is also compared with the Hirota bilinear operator technique.
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