Affiliation:
1. School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Abstract
Under this work, we derive a new fractal unsteady Korteweg–de Vries model which can model the shallow water with the non-smooth boundary. The generalized fractal variational principle is constructed by employing the semi-inverse method and the fractal two-scale transform. In addition, we also investigate the abundant exact solutions by means of the sub-equation method. The impact of the fractal orders on the behaviors of the solutions is also discussed in detail. The obtained variational principle reveals the energy form of the conservation laws in the fractal space, and the obtained solutions can help the researchers to study the properties of the fractal solitary wave in the extremely small scale of time and space.
Funder
Key Programs of Universities in Henan Province of China
Fundamental Research Funds for the Universities of Henan Province
Program of Henan Polytechnic University
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation
Cited by
22 articles.
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