Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves

Document Type : Research Paper


1 School of Science, Xi'an University of Architecture and Technology, Xi’an, China

2 University National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-Ai Road, Suzhou, China


The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of the equation.


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