SEMI-DOMAIN SOLUTIONS TO THE FRACTAL (3+1)-DIMENSIONAL JIMBO–MIWA EQUATION
Peng Xu, H. Huang, Hui Liu
Abstract
In this work, the variational direct method (VDM) based on the variational theory and Ritz-like method, combined with the fractal two-scale transformation, is employed to construct the semi-domain solutions of the (3+1)-dimensional fractal Jimbo–Miwa (JM) equation, which is derived by He’s fractal derivative. The applicability and effectiveness of the acquired solutions on the Cantor sets are presented through the numerical results in the form of 3-dimensional graphs. In addition, as a comparison, the exact solutions of the classic (3+1)-dimensional JM equation for [Formula: see text] are also illustrated. The obtained results in this work are expected to open new perspectives for the traveling wave theory.
Topics & Concepts
FractalDomain (mathematical analysis)MathematicsFractal derivativeTransformation (genetics)Work (physics)Mathematical analysisScale (ratio)Fractal analysisFractal dimensionPhysicsBiochemistryGeneChemistryQuantum mechanicsThermodynamicsNonlinear Waves and SolitonsFractional Differential Equations SolutionsAlgebraic structures and combinatorial models