New solitary and optical wave structures to the Korteweg-de Vries equation with dual-power law nonlinearity

In this manuscript, we apply the powerful sine-Gordon expansion method to the Korteweg-de Vries (KdV) equation with dual-power law nonlinearity. The method is a combination of the travelling wave transformation and sine-Gordon equation. We find some new complex solitary and optical wave solution structures to the KdV equation with dual-power law nonlinearity. Wolfram Mathematica 9 is used in carrying out all the computations and the graphics plot in this paper. We have finally submit a comprehensive conclusion.