Group analysis and modified extended tanh-function to find the invariant solutions and soliton solutions for nonlinear Euler equations

In this paper we find invariant solutions and soliton solutions for the nonlinear Euler equations with respect to the unknown functions G(x, y, t) and F(x, y, t). New dimensional reduction and exact solutions for nonlinear Euler equations are obtained. By using group analysis invariant solutions are given with respect to some forms of the unknown functions G(x, y, t) and F(x, y, t). We use the modified extended tanh- function to determine the soliton wave solutions for the nonlinear Euler equations.