Journal
WAVE MOTION
Volume 79, Issue -, Pages 84-97Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.wavemoti.2018.03.004
Keywords
Generalized discrete Hirota equation; Conservation laws; Modulational instability; Perturbation (n, N - n)-fold Darboux transformations; Discrete rogue waves
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Funding
- Qin Xin Talents Cultivation Program of Beijing Information Science and Technology University [QXTCP B201704, QXTCP A201702]
- China Postdoctoral Science Foundation [2015M570161]
- Beijing Natural Science Foundation [1153004, 1182009]
- National Natural Science Foundation of China [11375030, 11472315, 11401031]
- Beijing Great Wall Talents Cultivation Program [CITTCD20180325]
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This paper investigates the modulational instability and higher order-rogue waves in the generalized discrete Hirota system. The Lax pair and conservation laws for this system are constructed. Then the existent conditions for its modulational instability to form the rogue waves are given starting from the plane wave solution. Furthermore, the higher order discrete rogue waves of this system are reported using the novel discrete version of generalized perturbation (n, N - n)-fold Darboux transformation. Finally, the dynamical behaviors of the strong and weak interactions of these higher-order discrete rogue waves are discussed analytically and numerically, which exhibits abundant nonlinear wave structures. These results may be useful for understanding some physical phenomena in optical fibers and relevant fields. (C) 2018 Elsevier B.V. All rights reserved.
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