Chin. Phys. Lett.  2008, Vol. 25 Issue (2): 421-424    DOI:
Original Articles |
Inverse Scattering Transform for the Derivative Nonlinear Schrodinger Equation
YANG Chun-Nuan;YU Jia-Lu;CAI Hao;HUANG Nian-Ning
Department of Physics, Wuhan University, Wuhan 430072
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YANG Chun-Nuan, YU Jia-Lu, CAI Hao et al  2008 Chin. Phys. Lett. 25 421-424
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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.
Keywords: 05.45.Yv      42.81.Dp      42.65.-k     
Received: 19 October 2007      Published: 30 January 2008
PACS:  05.45.Yv (Solitons)  
  42.81.Dp (Propagation, scattering, and losses; solitons)  
  42.65.-k (Nonlinear optics)  
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Articles by authors
YANG Chun-Nuan
YU Jia-Lu
CAI Hao
HUANG Nian-Ning
[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
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