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On exact traveling-wave solutions for local fractional Korteweg-de Vries equation
Xiao-Jun Yang1, J A Tenreiro Machado2, Dumitru Baleanu3
1School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China.
Abstract:
This 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.
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