On exact traveling-wave solutions for local fractional Korteweg-de Vries equation

Xiao-Jun Yang; J A Tenreiro Machado; Dumitru Baleanu; Carlo Cattani

doi:10.1063/1.4960543

On exact traveling-wave solutions for local fractional Korteweg-de Vries equation

Chaos. 2016 Aug;26(8):084312. doi: 10.1063/1.4960543.

Authors

Xiao-Jun Yang¹, J A Tenreiro Machado², Dumitru Baleanu³, Carlo Cattani⁴

Affiliations

¹ School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China.
² Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. Antonio Bernardino de Almeida, 4249-015 Porto, Portugal.
³ Department of Mathematics, Faculty of Art and Sciences, Cankaya University, 06530 Balgat, Ankara, Turkey and Institute of Space and Sciences, Magurele-Bucharest, Romania.
⁴ Engineering School (DEIM), University of Tuscia, 01100 Viterbo, Italy.

PMID: 27586629
DOI: 10.1063/1.4960543

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.