Dynamics of rogue waves in the Davey–Stewartson II equation

By Yasuhiro Ohta, Jianke Yang. 2012

255 citations recorded by the source corpus.

General rogue waves in the Davey–Stewartson (DS)II equation are derived by the bilinear method, and the solutions are given through determinants. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background in a line profile and then retreat back to the constant background again. It is also shown that multi-rogue waves describe the interaction between several fundamental rogue waves, and higher order rogue waves exhibit different dynamics (such as rising from the constant background but not retreating back to it). Under certain parameter conditions, these rogue waves can blow up to infinity in finite time at isolated spatial points, i.e. exploding rogue waves exist in the DSII equation.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d6d0c69475a97a6b79d6cac3a09d2bbb43fb7de9

How researchers see this paper

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In Mathematical Physics

1. Bo Yang
2. Jianke Yang
3. Yong Chen

In Statistical and Nonlinear Physics

1. Bo Yang
2. Yong Chen
3. Jingsong He
4. Jianke Yang
5. Yi Cheng
6. Xin Wang
7. Jiguang Rao
8. Yuqi Li

Citations in the corpus

• Rational and Semirational Solutions of the Nonlocal Davey–Stewartson Equations (2017, background): “Thus these line waves possess a typical characteristic of the rogue wave: appearing from no where and disappearing without trace, hence they are line rogue waves [48,49].”
• Generalized Darboux transformation and localized waves in coupled Hirota equations (2013, background): “Many nonlinear single-componen t systems are found to possess rogue wave solution, the nonlinear Schrödinger (NLS) equation [12–21], the der ivative NLS equation [22, 23], the Hirota equation [24], the Sasa-Satsuma equation [25], the variable coe ffici nt NLS equation [26], the discrete NLS equation”
• Transformations between Nonlocal and Local Integrable Equations (2017, methodology): “These latter solutions have been reported in [29, 30].”