The Bi-Hamiltonian Structure and New Solutions of KdV6 Equation

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We show that the KdV6 equation and the nonholonomic perturbation of bi-Hamiltonian system of KdV hierarchy recently studied in Karasu-Kalkanli et al. (J Math Phys 49:073516, 2008) and Kupershmidt (Phys Lett A 372:2634–2639, 2008) are equivalent to the Rosochatius deformation of KdV equation and KdV hierarchy with self-consistent sources (RD-KdVESCS, RD-KdVHSCS), respectively, recently presented in Yao and Zeng (J Phys A Math Theor 41:295205, 2008). The t-type bi-Hamiltonian formalisms of KdV6 equation and RD-KdVHSCS are constructed by taking x as evolution parameter. Some new solutions of KdV6 equation, such as soliton, positon and negaton solution, are presented.

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