Travelling Solitary Wave Solutions to Non-Gaussian χ-Wick-Type Stochastic Burgers’ Equation with Variable Coefficients

In this work, we obtain non-Gaussian (NG) stochastic solutions to χ-Wick-type stochastic (χ-Wk-TS) Burgers’ equations with variable coefficients. An Exp-function method, the connection between white noise theory and hypercomplex systems (HCSs), the χ-Wick product (χ-Wk-product) and an χ-Hermite transform (χ-Hr-transform) are proposed. We provide a new set of non-Gaussian solitary wave solutions (NG-SWSs) to Burgers’ equations with variable coefficients. NG white noise functional solutions (NG-WNFSs) to χ-Wk-TS Burgers’ equations with variable coefficients are shown. The symmetry coefficients of partial differential equations and the symmetrical properties of SPDEs are critical in determining the best solution.