Complex travelling wave solutions to the KdV and Burgers equations

摘要

In the present work, making use of the hyperbolic tangent method, some complex travelling wave solutions to the Korteweg-deVries and Burgers equations are obtained. It is observed that the real part of the solution for the Burgers equation is of shock type whereas the imaginary part is the localized travelling wave. However, for the solution of the Korteweg-deVries equation the real part is a solitary wave while the imaginary part is the product of a solitary wave with a shock.