title: On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.
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.
authors: School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China.
authors: Xiao-Jun
authors: XJ
authors: Yang
authors: Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. Antonio Bernardino de Almeida, 4249-015 Porto, Portugal.
authors: J A
authors: JA
authors: Tenreiro Machado
authors: Department of Mathematics, Faculty of Art and Sciences, Cankaya University, 06530 Balgat, Ankara, Turkey and Institute of Space and Sciences, Magurele-Bucharest, Romania.
authors: Dumitru
authors: D
authors: Baleanu
authors: Engineering School (DEIM), University of Tuscia, 01100 Viterbo, Italy.
authors: Carlo
authors: C
authors: Cattani