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 (16)

• Deterministic Vector Freak Waves
• Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation
• General high-order rogue waves and their dynamics in the nonlinear Schroedinger equation
• Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium
• A generating mechanism for higher order rogue waves
• Rogue waves in the Davey-Stewartson equation
• Capillary rogue waves
• The Darboux transformation of the derivative nonlinear Schrödinger equation
• Freak waves in the linear regime: A microwave study
• Breather and Rogue Wave solutions of a Generalized Nonlinear Schrodinger Equation
• Rogue-wave solutions of a three-component coupled nonlinear Schrodinger equation
• The Rogue Wave and breather solution of the Gerdjikov-Ivanov equation
• Rogue waves of the Hirota and the Maxwell-Bloch equations
• Rogue waves of the Fokas-Lenells equation
• High-order rogue waves for the Hirota equation
• Two kinds of rogue waves of the general nonlinear Schrödinger equation with derivative

Cited by in corpus (14)

• Darboux transformation of nonisospectral coupled Gross-Pitaevskii equation and its multi-component generalization
• Rogue wave triggered at a critical frequency of a nonlinear resonant medium
• The height of an $n$th-order fundamental rogue wave for the nonlinear Schrödinger equation
• Families of exact solutions of a new extended (2+1)-dimensional Boussinesq equation
• Integrable nonlocal complex mKdV equation: soliton solution and gauge equivalence
• Construction of rational solutions of the real modified Korteweg-de Vries equation from its periodic solutions
• Rogue waves on an elliptic function background in complex modified Korteweg-de Vries equation
• Interaction phenomena between lump and solitary wave of a generalized (3 + 1)-dimensional variable-coefficient nonlinear-wave equation in liquid with gas bubbles
• Higher-order rogue wave dynamics for a derivative nonlinear Schrödinger equation
• Long time decay and asymptotics for the complex mKdV equation
• Families of rational and semi-rational solutions of the partial reverse space-time nonlocal Mel'nikov equation
• The general fifth-order nonlinear Schrödinger equation with nonzero boundary conditions: Inverse scattering transform and multisoliton solutions
• Spectral problem for the complex mKdV equation: singular manifold method and Lie symmetries
• On the evolution of a rogue wave along the orthogonal direction of the ($t,x$)-plane