N-soliton and quasi-periodic solutions of the KdV6 equations

A hierarchy of new nonlinear evolution equations which contains the well-known KdV6 equation is proposed. Based on the inverse scattering method, N-soliton solutions of the first four equations (including the KdV6 equation) in this hierarchy are derived. Finally, quasi-periodic solutions of the KdV6 equations are constructed according to the theory of algebraic curve.