Exact solutions of stochastic Burgers–Korteweg de Vries type equation with variable coefficients
Kolade Adjibi, Allan Martinez, Miguel Mascorro, Carlos Montes, Tamer Oraby, Rita Sandoval, Erwin Suazo
Abstract
We will present exact solutions for three variations of the stochastic Korteweg de Vries-Burgers (KdV-Burgers) equation featuring variable coefficients. In each variant, white noise exhibits spatial uniformity, and the three categories include additive, multiplicative, and advection noise. Across all cases, the coefficients are time-dependent functions. Our discovery indicates that solving certain deterministic counterparts of KdV-Burgers equations and composing the solution with a solution of stochastic differential equations leads to the exact solution of the stochastic Korteweg de Vries-Burgers (KdV-Burgers) equations.
Topics & Concepts
Burgers' equationKorteweg–de Vries equationMathematicsVariable (mathematics)Multiplicative functionWhite noiseStochastic differential equationMathematical analysisAdvectionApplied mathematicsPartial differential equationNonlinear systemPhysicsStatisticsQuantum mechanicsThermodynamicsNonlinear Dynamics and Pattern FormationFractional Differential Equations SolutionsFluid Dynamics and Turbulent Flows