Lie symmetry analysis of time fractional Burgers equation, Korteweg-de Vries equation and generalized reaction-diffusion equation with delays
Jicheng Yu
Abstract
In this paper, Lie symmetry analysis method is applied to time fractional Burgers equation, Korteweg-de Vries equation and generalized reaction-diffusion equation with delays, respectively. The Lie symmetries for fractional partial differential equations with delays (DFPDEs) are obtained, and the group classifications of the equations are established. The obtained group generators are used to reduce the DFPDEs to fractional ordinary differential equations with delays (DFODEs). Some exact solutions constructed for the DFODEs generate group-invariant solutions of the discussed DFPDEs.
Topics & Concepts
Burgers' equationMathematicsPartial differential equationLie groupKorteweg–de Vries equationHomogeneous spaceFirst-order partial differential equationKadomtsev–Petviashvili equationMathematical analysisMathematical physicsOrdinary differential equationDifferential equationInvariant (physics)Symmetry (geometry)Diffusion equationSymmetry groupFractional calculusRiccati equationPure mathematicsPhysicsNonlinear systemQuantum mechanicsGeometryEconomicsService (business)EconomyNonlinear Waves and SolitonsFractional Differential Equations SolutionsNonlinear Photonic Systems