摘要Since the Jost solutions of the derivative nonlinear Schrodinger equation do not tend to the free Jost solutions, when the spectral parameter tends to infinity(|λ| → ∞), the usual inverse scattering transform (IST) must be revised. If we take the parameter k=λ-1 as the basic parameter, the Jost solutions in the limit of |k → ∞), do tend to the free Jost solutions, hence the usual procedure to construct the equations of IST in k-plane remains effective. After we derive the equation of IST in terms of k, we can obtain the equation of IST in λ-plane by the simple change of parameters λ=kappa-1. The procedure to derive the equation of IST is reasonable, and attention is never paid to the function W(x) introduced by the revisions of Kaup and Newell. Therefore, the revision of Kaup and Newell can be avoided.
Abstract：Since the Jost solutions of the derivative nonlinear Schrodinger equation do not tend to the free Jost solutions, when the spectral parameter tends to infinity(|λ| → ∞), the usual inverse scattering transform (IST) must be revised. If we take the parameter k=λ-1 as the basic parameter, the Jost solutions in the limit of |k → ∞), do tend to the free Jost solutions, hence the usual procedure to construct the equations of IST in k-plane remains effective. After we derive the equation of IST in terms of k, we can obtain the equation of IST in λ-plane by the simple change of parameters λ=kappa-1. The procedure to derive the equation of IST is reasonable, and attention is never paid to the function W(x) introduced by the revisions of Kaup and Newell. Therefore, the revision of Kaup and Newell can be avoided.
[1]Kaup D J and Newell A C 1978 J. Math. Phys. 19798 [2]Huang N N 2007 Chin. Phys. Lett. 24 894 [3] Yang C N, Yu J L, Wang Q Q and Huang N N 2007 Commun.Theor. Phys. 48 299 [4]Mj$\phi$lhus E 1989 Physica Scripta 40 277 [5]Mj$\phi$lhus E and Hada T 1997 Nonlinear Waves andChaos in Space Plasmas ed Hada T and Matsumoto H (Tokyo: Terrapub)p 121 [6] Ruderman M S 2002 J. Plasma Phys. 67 271 [7] Chen X J and Lam W K 2004 Phys. Rev. E 69066604 [8] Chen X J, Yang J and Lam W K 2006 J. Phys. A 39 3263 [9] Cai H and Huang N N 2006 Int. J. Theor. Phys. 2 567 [10] Liu Y X, Yang B F and Cai H 2006 Int. J. Theor.Phys. 45 1855 [11] Chen X J, Hou L J and Lam W K 2005 Chin. Phys.Lett. 22 830
2008, Vol. 25 
