VARIATIONAL PRINCIPLE FOR A GENERALIZED KdV EQUATION IN A FRACTAL SPACE
Yue Shen, Ji‐Huan He
Abstract
A generalized KdV equation with fractal derivatives is suggested, and a special function is introduced to establish a fractal variational principle. A detailed derivation is elucidated step by step by the semi-inverse method, and some special cases are discussed.
Topics & Concepts
Korteweg–de Vries equationFractalVariational principleMathematicsMathematical analysisFractal derivativeSpace (punctuation)Applied mathematicsInverseLuke's variational principleFunction (biology)Fractal dimensionHamilton's principleClassical mechanicsFractal analysisPhysicsNonlinear systemComputer scienceGeometryEquations of motionQuantum mechanicsBiologyOperating systemEvolutionary biologyFractional Differential Equations SolutionsNonlinear Waves and SolitonsNonlinear Photonic Systems