We present a multiparameter family of a soliton on a background solution to the Sasa-Satsuma equation. The solution is controlled by a set of several free parameters that control the background amplitude as well as the soliton itself. This family of solutions admits a few nontrivial limiting cases that are considered in detail. Among these special cases is the nonlinear Schrödinger equation limit and the limit of rogue wave solutions.
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Bandelow et al. (2012) studied this question.
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