New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity

In this paper, we find new solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity according to the new extended direct algebraic method. When parameters involving this method are taken to be special values we can obtain the solitary wave solutions which is derived from other methods such as, the (G′/G)-expansion method, the modified Kudryashov method, the extended tanh-function method and so on. It is shown that the new extended direct algebraic method, with the help of symbolic computation, provides a more powerful mathematical tool for many other solving nonlinear partial differential equations.