Abstract
The modified Korteweg–de Vries (mKdV) and Maxwell–Bloch system is studied by using the dressing method based on the local 2 × 2 matrix -problem. By virtue of a singular dispersion relation, we derive the present mKdV equation with self-consistent sources which change the velocities of the solitons. The explicit solutions, including the bright and dark type N-soliton solutions due to different forms of the spectral transform matrix, are given by virtue of the properties of the Cauchy matrix.
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