Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...

Abstract— This paper describes Galerkin finite element (FEFLOW) models for the simulation of groundwater flow in twodimensional, transient, unconfined groundwater flow systems. This study involves validation of FEFLOW model with reported analytical solutions and also comparison of reported Explicit Finite Difference Model for groundwater flow simulation (FDFLOW). The model is further used to ob...

In the present paper the Analytical approximate solution of a fractional diffusion equation is deducedwith the help of powerful Variational Iterationmethod. By using an initial value, the explicit solutions of the equation for different cases have beenderived,which accelerate the rapid convergence of the series solution. The present method performs extremely well in terms of efficiency and simp...