title: 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 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.
authors.affiliation: Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China.
authors.forename: Jingsong
authors.initials: J
authors.lastname: He
authors.affiliation: Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China.
authors.forename: Lihong
authors.initials: L
authors.lastname: Wang
authors.affiliation: Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China.
authors.forename: Linjing
authors.initials: L
authors.lastname: Li
authors.affiliation: Department of Physics, Pondicherry University, Pondicherry 605014, India.
authors.forename: K
authors.initials: K
authors.lastname: Porsezian
authors.affiliation: Solar Physics and Space Plasma Research Centre, University of Sheffield, Sheffield S3 7RH, United Kingdom.
authors.forename: R
authors.initials: R
authors.lastname: Erdélyi
mesh_terms: D003198:Computer Simulation; D060733:Electromagnetic Radiation; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D055095:Optics and Photonics; D011789:Quantum Theory