Exact solutions for a Wick-type stochastic 2D KdV equation

Abundant solutions of Wick-type stochastic fractional 2D KdV equations

“…Broadly speaking, we generalize the work done by Elwakil et al [26] and Zhu et al [27] on the variable coefficients 2D KdV equations to new strategies that give white noise functional solutions of the variable coefficients Wick-type stochastic fractional 2D KdV equations. The strategies that will be pursued in our work rest mainly on Hermite transform, white noise theory, and modified fractional sub-equation method, all of which are employed to find white noise functional solutions of Eq.…”

“…, 15) give a new set of white noise functional solutions for the Wick-type stochastic 2D KdV equations. [27] Moreover the set of Hermit transforms u i = Ũi (z) (i = 1, 2, . .…”

Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion

“…To date, extensive research has been carried out on the complex nonlinear waves of KdV equations. Many methods have been developed to solve these equations, such as inverse scattering transformation [1], Darboux-Bäcklund transformation [2,3], Hirota's bilinear method [4,5], the first integral method [6], the homogeneous balance principle [7,8], the F-expansion method [9][10][11], the Wronskian method [12], the variational method [13], and Painlevé analysis [14]. On the other hand, KdV equations have different forms in different models, and the relevant methods were developed to study different types of KdV equations.…”