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

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 non-standard 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 RW of the complex mKdV and the NLS 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 ultra-short pulse technology.

31 pages, 22 figures, accepted by Phys.Rev.E

References in corpus (5)

• Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium
• Capillary rogue waves
• Rogue-wave solutions of a three-component coupled nonlinear Schrodinger equation
• Rogue waves of the Hirota and the Maxwell-Bloch equations
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Cited by in corpus (5)

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• Families of exact solutions of a new extended (2+1)-dimensional Boussinesq equation
• Integrable nonlocal complex mKdV equation: soliton solution and gauge equivalence
• Higher-order rogue wave dynamics for a derivative nonlinear Schrödinger equation
• Families of rational and semi-rational solutions of the partial reverse space-time nonlocal Mel'nikov equation