Exactly solvable variable parametric Burgers type models

Exactly solvable variable parametric Burgers type equations in one-dimension are introduced, and two different approaches for solving the corresponding initial value problems are given. The first one is using the relationship between the variable parametric models and their standard counterparts. The second approach is a direct linearization of the variable parametric Burgers model to a variable parametric parabolic model via a generalized Cole-Hopf transform. Eventually, the problem of finding analytic and exact solutions of the variable parametric models reduces to that of solving a corresponding second order linear ODE with time dependent coefficients. This makes our results applicable to a wide class of exactly solvable Burgers type equations related with the classical Sturm-Liouville problems for the orthogonal polynomials.