A KdV soliton propagating with varying velocity

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Abstract
Using one solution to the KdV equation found previously by Au and Fung [Phys. Rev. B 2 5, 6460 (1982)] we apply the Bäcklund transformation again to obtain a new set of solutions which are divergent at certain points in the special case where the vacuum parameter is zero. While one set of solutions is static, the other set is an asymptotic one‐soliton solution propagating with a varying velocity in a ‘‘transient’’ domain of space and time. To demonstrate the main features of our discovery, we have carried out a detailed numerical analysis of our analytical solutions.

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