We present a KdV-like 2-parameter equation ut + (3(1− δ)u+ (δ + 1)xx ux )ux = εuxxx. By using the dynamical system method, existence of different traveling wave solutions are discussed, including smooth solitary wave solution of with bell type, solitary wave solutions of valley type and peakon wave solution of valley type. Numerical integration are used to shown the different types of solutions...

The cubic complex one-dimensional Ginzburg–Landau equation is considered. Using the Hone’s method, based on the use of the Laurent-series solutions and the residue theorem, we have proved that this equation has neither elliptic standing wave no elliptic travelling wave solution. This result amplifies the Hone’s result, that this equation has no elliptic travelling wave solution.