A mixed nonlinear Schrödinger equation which has a usual cubic nonlinear term and a derivative cubic term is exactly solved by the inverse scattering method under the nonvanishing boundary condition. We obtain the soliton solution which generally pulsates. But it becomes stationary which is algebraic in some special cases. A peculiar structure of spiky modulation is also shown.
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Kawata et al. (1980) studied this question.
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