On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.
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DOI：
10.1063/1.4960543
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发表时间：
2016-08
期刊：
影响因子：
2.9
通讯作者：
Xiao-jun Yang;J. T. Tenreiro Machado;D. Baleanu;C. Cattani
中科院分区：
文献类型：
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作者：
Xiao-jun Yang;J. T. Tenreiro Machado;D. Baleanu;C. Cattani
本文在局部分数阶导数形式下研究了Korteweg-de弗里斯方程。分析了广义函数定义在Cantor集上的不可微型精确行波解。对分维为1时不可微解的结果也进行了讨论。结果表明，局部分数阶Korteweg-de弗里斯方程的精确解表征了浅水表面上的分形波.
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.