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The Solutions of the NLS Equations with Self-Consistent Sources

Yijun Shao·Yunbo Zeng
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Abstract

We construct the generalized Darboux transformation with arbitrary functions in time $t$ for the AKNS equation with self-consistent sources (AKNSESCS) which, in contrast with the Darboux transformation for the AKNS equation, provides a non-auto-Bäcklund transformation between two AKNSESCSs with different degrees of sources. The formula for N-times repeated generalized Darboux transformation is proposed. By reduction the generalized Darboux transformation with arbitrary functions in time $t$ for the Nonlinear Schrödinger equation with self-consistent sources (NLSESCS) is obtained and enables us to find the dark soliton, bright soliton and positon solutions for NLS$^{+}$ESCS and NLS$^{-}$ESCS. The properties of these solution are analyzed.

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Yijun Shao, Yunbo Zeng. 2004-12-29. The Solutions of the NLS Equations with Self-Consistent Sources. https://doi.org/10.1088/0305-4470%2F38%2F11%2F008

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