Nonlinear kinetic Alfven waves where beta much less than m(e)/m(i), have been solved both with and without the Poisson equation correction. It is found that the ratio of the perpendicular electric field and magnetic field, and the ratio of parallel and perpendicular electric field increase with deepening of the depressive density soliton. The former ratio may be larger than the Alfven velocity in the case of a large amplitude solitary kinetic Alfven wave. The Poisson equation correction is important for the nonlinear kinetic Alfven wave propagating along the magnetic field, which solves a puzzle of Sagdeev potential to approach infinity in the limit of K-x --> 0. This correction causes the solitary KAW possessing an electrostatic character along the direction of wave moving frame. These results have been compared with the observations from the Freja satellite in the low aurora.