Yang, Xiao-JunMachado, J. A. TenreiroBaleanu, DumitruCattani, Carlo2017-01-262016http://hdl.handle.net/10400.22/9448This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.engExact solutionsFractalsSurface wavesNavier Stokes equationsLaplace equationsjournal articlehttp://dx.doi.org/10.1063/1.4960543