Burgers equation with time-dependent coefficients and nonlinear forcing term: Linearization and exact solvability

We construct and discuss a linearization method for solving Burgers equation with time-dependent coefficients and a nonlinear forcing term. Our results are shown to contain and generalize recent findings (Miskinis, 2001; Buyukasik and Pashaev, 2013). As applications of our method we solve several initial- and boundary-value problems for Burgers equation with forcing of sinusoidal, polynomial, as well as X1-Laguerre exceptional orthogonal polynomial type.