School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Document Type
Article
Publication Date
11-25-2019
Abstract
The long-wave–short-wave (LWSW) model of Newell type is an integrable model describing the interaction between the gravity wave (long wave) and the capillary wave (short wave) for the surface wave of deep water under certain resonance conditions. In the present paper, we are concerned with rogue-wave solutions to the LWSW model of Newell type. By combining the Hirota’s bilinear method and the KP hierarchy reduction, we construct its general rational solution expressed by the determinant. It is found that the fundamental rogue wave for the short wave can be classified into three different patterns: bright, intermediate, and dark states, whereas the one for the long wave is always a bright state. The higher-order rogue wave corresponds to the superposition of fundamental ones. The modulation instability analysis shows that the condition of the baseband modulation instability where an unstable continuous-wave background corresponds to perturbations with infinitesimally small frequencies, coincides with the condition for the existence of rogue-wave solutions.
Recommended Citation
Chen, Junchao, Liangyuan Chen, Bao-Feng Feng, and Ken-ichi Maruno. 2019. “High-Order Rogue Waves of a Long-Wave--Short-Wave Model of Newell Type.” Physical Review E 100 (5): 052216. https://doi.org/10.1103/PhysRevE.100.052216.
Publication Title
Physical Review E
DOI
10.1103/PhysRevE.100.052216
Comments
©2019, American Physical Society. Original published version available at https://doi.org/10.1103/PhysRevE.100.052216