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Few-cycle optical rogue waves: Complex modified Korteweg-de Vries equation

He, Jingsong and Wang, Lihong and Li, Linjing and Porsezian, K. and Erdélyi, Róbert (2014) Few-cycle optical rogue waves: Complex modified Korteweg-de Vries equation. PHYSICAL REVIEW E - STATISTICAL, NONLINEAR AND SOFT MATTER PHYSICS (2001-2015), 89 (6). ISSN 1539-3755

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Abstract

In this paper, we consider the complex modified Korteweg-de Vries (mKdV) equation as a model of few-cycle optical pulses. Using the Lax pair, we construct a generalized Darboux transformation and systematically generate the first-, second-, and third-order rogue wave solutions and analyze the nature of evolution of higher-order rogue waves in detail. Based on detailed numerical and analytical investigations, we classify the higher-order rogue waves with respect to their intrinsic structure, namely, fundamental pattern, triangular pattern, and ring pattern. We also present several new patterns of the rogue wave according to the standard and nonstandard decomposition. The results of this paper explain the generalization of higher-order rogue waves in terms of rational solutions. We apply the contour line method to obtain the analytical formulas of the length and width of the first-order rogue wave of the complex mKdV and the nonlinear Schrödinger equations. In nonlinear optics, the higher-order rogue wave solutions found here will be very useful to generate high-power few-cycle optical pulses which will be applicable in the area of ultrashort pulse technology.

Item Type: Article
Uncontrolled Keywords: DNA; SOLITONS; Tunneling Josephson effect Bose-Einstein condensates in periodic potentials solitons vortices and topological excitations; nonlinear guided waves; Optical solitons;
Subjects: Q Science / természettudomány > QC Physics / fizika
SWORD Depositor: MTMT SWORD
Depositing User: MTMT SWORD
Date Deposited: 26 Feb 2024 14:23
Last Modified: 26 Feb 2024 14:23
URI: https://real.mtak.hu/id/eprint/189010

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