EXACT TRAVELING-WAVE SOLUTIONS FOR ONE-DIMENSIONAL MODIFIED KORTEWEG–DE VRIES EQUATION DEFINED ON CANTOR SETS-Reference-Cited by-同舟云学术

EXACT TRAVELING-WAVE SOLUTIONS FOR ONE-DIMENSIONAL MODIFIED KORTEWEG–DE VRIES EQUATION DEFINED ON CANTOR SETS

Published:2019-02 Issue:01 Volume:27 Page:1940010
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

GAO FENG¹²,YANG XIAO-JUN¹²³,JU YANG¹⁴

Affiliation:

1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China

2. School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, P. R. China

3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, P. R. China

4. State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology at Beijing, Beijing 100083, P. R. China

Abstract

The one-dimensional modified Korteweg–de Vries equation defined on a Cantor set involving the local fractional derivative is investigated in this paper. With the aid of the fractal traveling-wave transformation technology, the nondifferentiable traveling-wave solutions for the problem are discussed in detail. The obtained results are accurate and efficient for describing the fractal water wave in mathematical physics.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X19400103

Reference31 articles.

1. Application of fractal concepts to polymer statistics and to anomalous transport in randomly porous media

2. Pore-Scale Viscous Fingering in Porous Media

3. Dynamical Transition in Quasistatic Fluid Invasion in Porous Media

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5. Fractal analysis of invasion depth of extraneous fluids in porous media

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