Abstract
We discuss the Darboux transformation method for a modified Korteweg–de Vries equation with variable coefficients and perturbing terms in detail based on the general form of the Darboux transformations for some nonlinear evolution equations solvable by the Ablowitz–Kaup–Newell–Segur inverse scattering method. We use this method to generate families of two-soliton solutions and two-periodic solutions.
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