Abstract
In the present investigation, the breathers and rogue waves on the double-periodic background are successfully constructed by Darboux transformation using a plane wave seed solution. Firstly, the Darboux transformation for the reverse-space-time derivative nonlinear Schrödinger equation is constructed. Secondly, periodic solutions, breathers, double-periodic solutions, breathers on the periodic and double-periodic background are derived by n-fold Darboux transformation. Thirdly, the higher-order rogue waves on the periodic and double-periodic background are constructed by semi-degenerate Darboux transformation. In addition, the dynamic behaviors of the solutions are plotted to show some interesting new solution structures.
Highlights
Nonlinear evolution equations play an important role and their solutions have been a hot research spot, including soliton [1, 2, 3, 4], breather [5, 6, 7], rogue wave [8, 9, 10, 11] and others [12, 13, 14, 15]
The breathers and rogue waves on the double-periodic background for Eq(2) have been constructed, which are first generated by plane wave seed solution
We have found the breathers on the double-periodic background more observed in the t direction by dynamics analysis
Summary
Nonlinear evolution equations play an important role and their solutions have been a hot research spot, including soliton [1, 2, 3, 4], breather [5, 6, 7], rogue wave [8, 9, 10, 11] and others [12, 13, 14, 15]. In [37], the periodic bounded solutions of the second-type nonlocal DNLS equation from zero seed solutions have been studied. In [46, 47], the rogue waves on the periodic background are constructed by generalized DT of odd order. We construct breathers on periodic and double-periodic background for the reverse-space-time DNLS equation by N -fold DT. By taking the dynamics analysis of the rogue waves on double-periodic background, we show two types of structure: the two peak and four peak.
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