Abstract
The solutions of KdV studied in Kovalyov [Kovalyov M. On a class of solutions of KdV. J Differ Equations 1951;15:309–60; Kovalyov M. Basic motions of the Korteweg–de Vries equation, Nonlinear Anal Theory Methods Appl 1998;31(5/6):599–619; Kovalyov M. Modulating properties of harmonic breather solutions of KdV. J Phys A: Math Gen 1998;31:5117–28.] exhibit wave–particle behavior albeit somewhat different from the wave–particle behavior of quantum mechanics . Yet the balance between the wave and particle properties of these solutions is governed by an uncertainty principle remarkably similar to that of quantum mechanics.
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