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/content/aip/journal/chaos/26/8/10.1063/1.4960543
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/content/aip/journal/chaos/26/8/10.1063/1.4960543
2016-08-08
2016-12-11

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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