Soliton Solutions to a Nonisospectral mKdV-sG Equation with Self-Consistent Sources and Reductions

We derive multisoliton solutions for a nonisospectral mKdV-sG equation with self-consistent sources by means of the bilinear approach. This nonisospectral equation is a generic one which is related to a time-dependent spectral parameter with time evolution λt=μ2λ+4μ3λ3+ν2/(4λ). Reductions to some soliton equations with self-consistent sources are investigated. One- and two-soliton solutions for the reduced equations are presented and dynamical behaviors are illustrated.