A NEW PERSPECTIVE TO STUDY THE THIRD-ORDER MODIFIED KDV EQUATION ON FRACTAL SET
Jian‐Gen Liu, Xiao‐Jun Yang, Yi‐Ying Feng, Ping Cui
Abstract
In this paper, we construct the Bäcklund transformations and the super-position formulas to the constant coefficients local fractional Riccati equation for the first time. Next, by means of the Bäcklund transformations and seed solutions which have been known in [X. J. Yang et al., Non-differentiable solutions for local fractional nonlinear Riccati differential equations, Fundam. Inform. 151(1–4) (2017) 409–417], we can get a class of exact solutions to the third-order modified KdV equation on the fractal set. These new type solutions can assist us to review different nonlinear phenomena better, which had been modeled via local fractional derivative.
Topics & Concepts
MathematicsKorteweg–de Vries equationRiccati equationNonlinear systemDifferentiable functionFractalMathematical analysisOrdinary differential equationType (biology)Position (finance)Differential equationApplied mathematicsSet (abstract data type)Order (exchange)PhysicsEcologyFinanceEconomicsComputer scienceQuantum mechanicsProgramming languageBiologyFractional Differential Equations SolutionsNonlinear Waves and SolitonsAdvanced Differential Equations and Dynamical Systems