Discrete Hirota equation: discrete Darboux transformation and new discrete soliton solutions
Under investigation in this paper is the discrete Hirota equation which is a combination of discrete NLS and discrete complex modified KdV equations. The discrete spectral problem analysis has been made, and discrete Darboux transformation(DT) has been constructed based on \(2\times 2\) discrete Lax pair for system (1.3). In addition, we have derived new discrete one-soliton solutions by using the obtained discrete DT for system (1.3). Figures have been plotted to display the dynamic features of discrete solitons.
KeywordsDiscrete Hirota equation Soliton Discrete Darboux transformation
We express our sincere thanks to each member of our discussion group for their suggestions. This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11347165 and 61405137, by the Shanxi Province Science Foundation for Youths under Grant Nos. 2015021008 and by Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi under Grant No.2013110.
- 26.Gu, C.H., He, H.S., Zhou, Z.X.: Darboux Transformation in Soliton Theory and Its Geometric Applications. Shanghai Scientific and Technical Publishers, Shanghai (2005)Google Scholar