a Department of Physics, Wuhan University, Wuhan 430072, China; b Department of Physics, Guangzhou Normal University, Guangzhou 510400, China; c Department of Physics, Jinan University, Guangzhou 510632, China
Abstract Based on the Zakharov-Shabat equation of the inverse scattering transform for the unstable nonlinear Schr$\ddot{\rm o}$dinger equation, for which a perturbation theory with corrections is developed in this paper. All necessary formulae for calculating the scattering data are derived. Based upon these formulae, the effect due to the corrections can be studied. As an example, the correction due to the damping is calculated.
Received: 23 July 1998
Accepted manuscript online:
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