Yang Xiao-Jun, Tenreiro Machado J A, Baleanu Dumitru, Cattani Carlo
School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China.
Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. Antonio Bernardino de Almeida, 4249-015 Porto, Portugal.
Chaos. 2016 Aug;26(8):084312. doi: 10.1063/1.4960543.
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.
本文在局部分数阶导数公式的范围内研究了科特韦格 - 德弗里斯方程。分析了在康托集上定义的广义函数的不可微类型的精确行波解。还讨论了分形维数为1时不可微解的结果。结果表明，局部分数阶科特韦格 - 德弗里斯方程的精确解表征了浅水面上的分形波。
