Abstract
The second-type derivative nonlinear Schrödinger (DNLSII) equation was introduced as an integrable model in 1979. Very recently, the DNLSII equation has been shown by an experiment to be a model of the evolution of optical pulses involving self-steepening without concomitant self-phase-modulation. In this paper, the n-fold Darboux transformation (DT) T n of the coupled DNLSII equations is constructed in terms of determinants. Comparing with the usual DT of the soliton equations, this kind of DT is unusual because T n includes complicated integrals of seed solutions in the process of iteration. By a tedious analysis, these integrals are eliminated in T n except the integral of the seed solution. Moreover, this T n is reduced to the DT of the DNLSII equation under a reduction condition. As applications of T n , the explicit expressions of soliton, rational soliton, breather, rogue wave and multi-rogue wave solutions for the DNLSII equation are displayed.
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Zhang, Y., Guo, L., He, J. et al. Darboux Transformation of the Second-Type Derivative Nonlinear Schrödinger Equation. Lett Math Phys 105, 853–891 (2015). https://doi.org/10.1007/s11005-015-0758-x
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DOI: https://doi.org/10.1007/s11005-015-0758-x