Elliptic solutions for higher order KdV equations

We study higher order KdV equations from the GL(2, R) congruent to SO(2,1) Lie group point of view. We find elliptic solutions of higher order KdV equations up to the ninth order. We argue that the main structure of the trigonometric/hyperbolic/elliptic N-soliton solutions for higher order KdV equations is the same as that of the original KdV equation. Pointing out that the difference is only the time dependence, we find N-soliton solutions of higher order KdV equations can be constructed from those of the original KdV equation by properly replacing the time-dependence. We discuss that there always exist elliptic solutions for all higher order KdV equations.