Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves
Ji‐Huan He
Abstract
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.
Topics & Concepts
Korteweg–de Vries equationFractalMathematicsBurgers' equationWaves and shallow waterVariational principleMathematical analysisMathematical physicsApplied mathematicsPhysicsThermodynamicsNonlinear systemPartial differential equationQuantum mechanicsNonlinear Waves and SolitonsOcean Waves and Remote SensingFractional Differential Equations Solutions