Abstract
Two non-isospectral KdV equations with self-consistent sources are derived. Gauge transformation between the first non-isospectral KdV equation with self-consistent sources (corresponding to λt = −2aλ) and its isospectral counterpart is given, from which exact solutions for the first non-isospectral KdV equation with self-consistent sources is easily listed. Besides, the soliton solutions for the two equations are obtained by means of Hirota's method and Wronskian technique, respectively. Meanwhile, the dynamical properties for these solutions are investigated.
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