BINARY REPRODUCING KERNEL HILBERT SPACE APPROACH FOR SOLVING WICK TYPE STOCHASTIC KDV EQUATION

Abstract

In this work, we aim at applying an appropriate kernelization approach to solve analytically the Wicktype
stochastic Korteweg-de Vries (KdV) equation with variable coefficients. Per the benefit of
formulating the problem in Hilbert space, we deliver a binary reproducing kernel Hilbert space (RKHS)
structure to represent the solution of such problem in the suggested kernel Hilbert space. Implying
Hermite transform, white noise theory and proper binary reproducing kernel Hilbert spaces, we articulate
white noise functional solutions for the Wick-type stochastic KdV equations. Representation of the exact
solution is given in some reproducing kernel space. The uniform convergence, of the approximate
solution together with its first derivative utilizing the suggested scheme, is investigated. The relevance of
our suggested approach is inspected partially on one of the most important spectral density study, namely
the cross power spectral density (CPSD) attests to the reliability of the scheme and highlighted the worth
of the present work that can be applied on a wide class of nonlinear partial differential emerge in
numerous physical modeling phenomena.