EXACT TRAVELING WAVE SOLUTIONS FOR THE LOCAL FRACTIONAL KADOMTSOV–PETVIASHVILI–BENJAMIN–BONA–MAHONY MODEL BY VARIATIONAL PERSPECTIVE
Kang‐Le Wang
Abstract
In this work, the Kadomtsov–Petviashvili–Benjamin–Bona–Mahony model is described by the local fractional derivative (LFD) on Cantor sets. A novel algorithm is presented to seek the exact traveling wave solution of the nondifferentiable type for the local fractional Kadomtsov–Petviashvili–Benjamin–Bona–Mahony model based on the variational theory, which is called variational wave transform method (VWTM). This new algorithm provides a new idea for seeking the exact traveling wave solutions in fractal space with simplicity and efficiency. The physical properties of traveling wave solutions are described by some 3D simulation figures.
Topics & Concepts
MathematicsFractalTraveling waveFractional calculusPerspective (graphical)Mathematical analysisSpace (punctuation)Exact solutions in general relativityWork (physics)Type (biology)SimplicityApplied mathematicsGeometryPhysicsComputer scienceBiologyEcologyOperating systemThermodynamicsQuantum mechanicsFractional Differential Equations SolutionsNonlinear Waves and SolitonsAdvanced Differential Equations and Dynamical Systems