VARIATIONAL PRINCIPLES FOR FRACTAL WHITHAM–BROER–KAUP EQUATIONS IN SHALLOW WATER
Kang‐Jia Wang, Kang‐Le Wang
Abstract
In this paper, we mainly consider the Whitham–Broer–Kaup equations with unsmooth boundaries, and a new fractal derivative is adopted to construct the fractal model. The variational principles of the fractal Whitham–Broer–Kaup equations are successfully constructed by fractal Semi-inverse method, which is helpful to study the symmetry, discover the conserved quantity, and has a wide application prospect in numerical simulation. The results are discussed by the two-scale transform method. The approximate analytical solutions of the fractal Whitham–Broer–Kaup equations are obtained according to the variational iteration method and two-scale transform method.
Topics & Concepts
FractalMathematicsScale (ratio)InverseWaves and shallow waterMathematical analysisApplied mathematicsFractal derivativeShallow water equationsSymmetry (geometry)Fractal analysisFractal dimensionGeometryPhysicsQuantum mechanicsThermodynamicsFractional Differential Equations SolutionsNonlinear Waves and SolitonsStatistical Mechanics and Entropy