Decay mode solution of nonlinear boundary-initial value problems for the cylindrical (spherical) Boussinesq-Burgers equations

The major target of this paper is to construct new nonlinear boundary-initial value problems for Boussinesq-Burgers Equations, and derive the solutions of these nonlinear boundary-initial value problems by the simplified homogeneous balance method. The nonlinear transformation and its inversion between the Boussinesq-Burgers Equations and the linear heat conduction equation are firstly derived; then a new nonlinear boundary-initial value problem for the Boussinesq-Burgers equations with variable damping on the half infinite straight line is put forward for the first time, and the solution of this nonlinear boundary-initial value problem is obtained, especially, the decay mode solution of nonlinear boundary-initial value problem for the cylindrical (spherical) Boussinesq-Burgers equations is obtained.