Exact Solutions for a System of KdV Equations with Some Applications of White-Noise Analysis

Applied functional analysis has many applications in other branches of mathematics such as differential equations numerical analysis stochastic calculus calculus of variations quantum field theory etc. Among of these applications we interest in stochastic differential equations (SDEs). In particular if we allow for some randomness in some of the coefficients of a partial differential equation (PDE) we often obtain a more realistic mathematical model of the situation. This model would be PDE involving stochastic parameters - stochastic partial differential equation (SPDE). Representative examples are the stochastic Korteweg-de Vries (KdV) equations.