The management and containment of self-similar rogue waves in the inhomogeneous nonlinear Schrödinger equation

Dai, Chao-Qing; Wang, Yueyue; Tian, Qing; Zhang, Jie-Fang

doi:10.1016/j.aop.2011.11.016

Cited by 119 publications

(69 citation statements)

References 48 publications

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“…Recently, enigmas of optical and matter-wave soliton nonlinear tunnelling have also been uncovered in [12]. More recently, Dai et al [13] and Zhu [14] investigated controllable rogue waves tunnelling through the NW and NB in 1 þ1 and 2 þ1 dimensions, respectively.…”

Section: Introductionmentioning

confidence: 97%

Nonlinear tunnelling of superposed Akhmediev breather in PT-symmetric inhomogeneous nonlinear couplers with gain and loss

Zhou

Dai

Chen

2015

Optics Communications

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Section: Introductionmentioning

confidence: 97%

Nonlinear tunnelling of superposed Akhmediev breather in PT-symmetric inhomogeneous nonlinear couplers with gain and loss

Zhou

Dai

Chen

2015

Optics Communications

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“…The formation of rogue waves in nonlinear dispersive media can be described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger (NLS) equation [8][9][10]13], which has the analytic solutions in the forms of certain types of breathers or solitons on the finite background, i.e., the Akhmediev breathers (ABs), Kuznetsov-Ma (KM) solitons and Peregrine solitons [8][9][10][11][12]. Such solutions allow the analytic studies into the conditions that support the emergence of rogue waves [8][9][10][11][12]14,15].…”

Section: Introductionmentioning

confidence: 99%

Breathers and rogue waves of the fifth-order nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain

et al. 2015

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One-dimensional anisotropic Heisenberg ferromagnetic spin chain can be described by the fifthorder nonlinear Schrödinger equation, which is investigated in this paper. Through the Darboux transformation, we obtain the Akhmediev breathers (ABs), Kuznetsov-Ma (KM) solitons and rogue-wave solutions. Effects of the coefficients of the fourth-order dispersion, γ , and of the fifth-order dispersion, δ, on the properties of ABs, KM solitons and rogue waves are discussed: (1) With γ increasing, the AB exhibits stronger localization in time; (2) The propagation directions of an AB and a KM soliton change with the presence of δ; and (3) Enhancement of γ makes the existence time of the rogue waves shorter, while enhancement of δ increases the existence time of the rogue waves.

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“…Therefore, some authors discussed the controllable behaviors of RWs [20][21][22][23]. The management and containment of selfsimilar picosecond [20,21] and femtosecond [22] RWs in the inhomogeneous NLSE were investigated, respectively. Moreover, controllable RW triplets have been discussed [23].…”

Section: Introductionmentioning

confidence: 99%

Superposed Kuznetsov-Ma solitons in a two-dimensional graded-index grating waveguide

Dai

Zhu

2013

J. Opt. Soc. Am. B

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The 2 1-dimensional coupled nonlinear Schrödinger equation with distributed coefficients in a graded-index grating waveguide is investigated, and an exact two-breather solution for certain functional relations is obtained. From this solution, the superposed Kuznetsov-Ma (KM) solitons can be constructed. The explicit functions that describe the evolution of the peak, width, center, and phase are found exactly, from which one knows that diffraction and chirp factors play important roles in the evolutional characteristics, such as phase, center and widths, while the gain/loss parameter only affects the evolution of their peaks. Moreover, we can change the propagation type of the superposed KM solitons by adjusting the relation between the maximum effective propagation distance Z m and the periodic locations Z ij based on the maximum amplitude of the superposed KM solitons. The controllability for the type of excitation, such as partial excitation, maintenance, and postponement of the superposed KM solitons, is exhibited.

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The management and containment of self-similar rogue waves in the inhomogeneous nonlinear Schrödinger equation

Cited by 119 publications

References 48 publications

Nonlinear tunnelling of superposed Akhmediev breather in PT-symmetric inhomogeneous nonlinear couplers with gain and loss

Nonlinear tunnelling of superposed Akhmediev breather in PT-symmetric inhomogeneous nonlinear couplers with gain and loss

Breathers and rogue waves of the fifth-order nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain

Superposed Kuznetsov-Ma solitons in a two-dimensional graded-index grating waveguide

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