Infinitely many new solutions and the closed form of the solution for initial-value problem of the Burgers equation

Infinitely many simple-solitary-wave solutions and infinitely many rational function solutions, especially the Hopf–Cole’s transformation and the closed form of the solution for initial-value problem of the Burgers equation, are obtained by using the extended homogeneous balance method. The method which is used here is simple and can be generalized to deal with other classes of nonlinear equations.