Darboux transformation of a new generalized nonlinear Schrödinger equation: soliton solutions, breather solutions, and rogue wave solutions
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In this paper, a new generalized nonlinear Schrödinger (GNLS) equation is investigated by Darboux matrix method. Firstly, the n-fold Darboux transformation (DT) of the GNLS equation is constructed. Then, the soliton solutions, breather solutions, and rogue wave solutions of the GNLS equation are studied based on the DT by choosing different seed solutions. Furthermore, the dynamic features of these solutions are explicitly delineated through some figures with the help of Maple software.
KeywordsGeneralized nonlinear Schrödinger equation Darboux transformation Soliton solutions Breather solutions Rogue wave solutions
Thank our partners for their help. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Especially, we are very grateful to the editor and reviewers for their constructive comments and suggestions. This research has been supported by the Natural Science Basic Research Program of Shaanxi (No. 2017JM1024).
- 17.Akhmediev, N.N., Korneev, V.I., Mitskevich, N.V.: N-modulation signals in a single-mode optical fiber with allowance for nonlinearity. Zhurnal Eksperimentalnoi I Teroreticheskoi Fiziki 94(1), 159–170 (1988)Google Scholar
- 26.Rao, J.G., Liu, Y.B., Qian, C., He, J.S.: Rogue waves and hybrid solutions of the Boussinesq equation. Z. Fr. Naturforschung A 72(4), 026601 (2017)Google Scholar
- 28.He, J., Xu, S., Porsezian, K.: Rogue waves of the Fokas–Lenells equation. J. Phys. Soc. Jpn. 81(12), 4007 (2012)Google Scholar
- 30.Chen, S., Song, L.: Rogue waves in coupled Hirota systems. Phys. Rev. E Stat. Phys. Plasmas, Fluids 87(87), 83–99 (2013)Google Scholar
- 33.Chen, J., Chen, Y., Feng, B.F., Maruno, K.: Rational solutions to multicomponent Yajima–Oikawa systems: from two dimension to one dimension. Physics 40(Suppl 4), 737–756 (2014)Google Scholar
- 37.Gu, C., Hu, H., Zhou, Z.: Darboux Transformations in Integrable Systems. Springer, Berlin (2004)Google Scholar