Closed-form solutions of stochastic KdV equation with generalized conformable derivatives
Ahmed H. Soliman, Abd‐Allah Hyder
Abstract
Abstract With the assistance of Hermite transform, we use the Exp-function technique to solve the Wick-type stochastic KdV equation with a generalized type of conformable derivatives. The exact solutions of the stochastic KdV equation are obtained in a white noise environment. Two new kinds of Brownian motion functional solutions, including soliton and periodic solutions are presented. The graphs for a portion of these exact solutions have been given by picking peculiar values of the existing parameters to visualize the proposed technique of the given KdV equation.
Topics & Concepts
Conformable matrixKorteweg–de Vries equationHermite polynomialsType (biology)Brownian motionWhite noiseSolitonMathematicsNoise (video)Applied mathematicsMathematical analysisPhysicsComputer scienceNonlinear systemQuantum mechanicsBiologyStatisticsEcologyArtificial intelligenceImage (mathematics)Nonlinear Waves and SolitonsNonlinear Photonic SystemsFractional Differential Equations Solutions