TY - JOUR
T1 - High-order rogue waves of a long-wave-short-wave model of Newell type
AU - Chen, Junchao
AU - Chen, Liangyuan
AU - Feng, Bao Feng
AU - Maruno, Ken Ichi
N1 - Funding Information:
J.C. expresses his sincere thanks to Profs. L. Ling, J. Yang, and Y. Ohta for their enthusiastic support and useful suggestions. J.C. acknowledges the support from NSF of China (Grant No.11705077). B.-F. acknowledges the partial support from NSF (Grant No. DMS-1715991) and NSF of China (Grant No. 11728103). K.M.'s work was supported by JSPS Grant-in-Aid for Scientific Research (Grant No. C-15K04909) and JST CREST.
Publisher Copyright:
©2019 American Physical Society.
PY - 2019/11/25
Y1 - 2019/11/25
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevE.100.052216
DO - 10.1103/PhysRevE.100.052216
M3 - Article
C2 - 31869955
AN - SCOPUS:85075570057
VL - 100
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
SN - 1063-651X
IS - 5
M1 - 052216
ER -