Solutions of a system of forced Burgers equation

In this article, we obtain explicit solutions of a system of forced Burgers equation subject to some classes of bounded and compactly supported initial data and also subject to certain unbounded initial data. In a series of papers, Rao and Yadav (2010) [1–3] obtained explicit solutions of a nonhomogeneous Burgers equation in one dimension subject to certain classes of bounded and unbounded initial data. Earlier Kloosterziel (1990) [4] represented the solution of an initial value problem for the heat equation, with initial data in L2(Rn,e|x|2/2)L2(Rn,e|x|2/2), as a series of self-similar solutions of the heat equation in RnRn. Here we express the solutions of certain classes of Cauchy problems for a system of forced Burgers equation in terms of self-similar solutions of some linear partial differential equations.