Abstract
The unstable nonlinear Schrödinger (NLS) equation is solved by the inverse scattering transform. Based on the constructed Zakharov–Shabat equation, it is shown that the soliton solution of the unstable NLS equation can be known from the soliton solution of the usual NLS equation by simply exchanging the tariables. The explicit N-soliton solution and the position shifts due to the collision are thus calculated.
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