Rogue wave solutions in AB system
Xin Wang, Yuqi Li, Yong Chen
TL;DR
This paper develops a generalized Darboux transformation for the AB system, deriving explicit rogue wave solutions with free parameters, and illustrating their complex dynamics and structures.
Contribution
It introduces a unified formula for Nth-order rogue wave solutions in the AB system using a direct iterative rule, including first and second order cases.
Findings
Derived explicit rogue wave solutions with free parameters.
Illustrated complex rogue wave dynamics and structures.
Provided a unified approach for higher-order rogue waves.
Abstract
In this paper, the generalized Darboux transformation is established to the AB system, which mainly describes marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics. We find a unified formula of Nth-order rogue wave solution for the AB system by the direct iterative rule. In particular, rogue waves possessing several free parameters from first to second order are calculated. The dynamics and some interesting structures of the rogue waves are illustrated through some figures.
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Fractional Differential Equations Solutions