Numerical Solutions of Variable-Coefficient Fractional-in-Space KdV Equation with the Caputo Fractional Derivative
Han Che, Yulan Wang
Abstract
In this paper, numerical solutions of the variable-coefficient Korteweg-De Vries (vcKdV) equation with space described by the Caputo fractional derivative operator is developed. The propagation and interaction of vcKdV equation in different cases, such as breather soliton and periodic suppression soliton, are numerically simulated. Especially, the Fourier spectral method is used to solve the fractional-in-space vcKdV equation with breather soliton. From numerical simulations and compared with other methods, it can be easily seen that our method has low computational complexity and higher precision.
Topics & Concepts
Korteweg–de Vries equationSolitonBreatherMathematicsFractional calculusMathematical analysisSpace (punctuation)Variable (mathematics)Operator (biology)Variable coefficientNumerical analysisDerivative (finance)PhysicsNonlinear systemQuantum mechanicsBiochemistryChemistryLinguisticsEconomicsPhilosophyGeneRepressorFinancial economicsTranscription factorNonlinear Waves and SolitonsFractional Differential Equations SolutionsNonlinear Photonic Systems