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Darboux transformations for super-Schrödinger equation, super-Dirac equation and their exact solutions

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Abstract

The Darboux transformation (DT) for the super-integrable hierarchy has an essential difference from the general system. As we know, the super-integrable soliton equation hierarchies with four potentials are discussed. Starting from the spectral problems of super-AKNS hierarchy and super-Dirac hierarchy, a DT method for two super-integrable hierarchies is constructed, which is more complex than the general integrable system. Soliton solutions of super-Schrödinger equation and super-Dirac equation are presented by using DT, which contain some bright, dark and breather wave soliton solutions. Then, the properties of these solutions in the inhomogeneous media are discussed graphically to illustrate the influences of the variable coefficients.

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Acknowledgements

This work was supported by the Natural Science Foundation of Liaoning Province, China (Grant No. 201602678).

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  1. School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang, 110034, China

    Fajun Yu, Lili Feng & Li Li

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  1. Fajun Yu
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Yu, F., Feng, L. & Li, L. Darboux transformations for super-Schrödinger equation, super-Dirac equation and their exact solutions. Nonlinear Dyn 88, 1257–1271 (2017). https://doi.org/10.1007/s11071-016-3308-x

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