The stochastic soliton-like solutions of stochastic KdV equations

By means of a generalized method and symbolic computation, we consider a stochastic KdV equation Ut + f(t)U Ux + g(t)Uxxx = W(t) R (t, U, Ux, Uxxx). We construct new and more general formal solutions. At the same time, we recover all the solutions found by Xie [Phys. Lett. A 310 (2003) 161]. The solutions obtained include the nontravelling wave and coefficient function’s stochastic soliton-like solutions, singular stochastic soliton-like solutions, stochastic triangular functions solutions.