Managements of scalar and vector rogue waves in a partially nonlocal nonlinear medium with linear and harmonic potential
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ORIGINAL PAPER
Managements of scalar and vector rogue waves in a partially nonlocal nonlinear medium with linear and harmonic potentials Chao-Qing Dai · Yue-Yue Wang · Jie-Fang Zhang
Received: 24 June 2020 / Accepted: 7 September 2020 © Springer Nature B.V. 2020
Abstract We consider a (2 + 1)-dimensional nonautonomous-coupled nonlinear Schrödinger equation, which includes the partially nonlocal nonlinearity under linear and harmonic potentials. Via a projecting expression between nonautonomous and autonomous equations, and utilizing the bilinear method and Darboux transformation method, we find diversified exact solutions. These solutions contain the nonlocal rogue wave and Akhmediev or Ma breather solutions, and the combined solution which describes a rogue wave superposed on an Akhmediev or Ma breather. By adjusting values of diffraction, width and phase chirp parameters of wave, the maximum value of the accumulated time can be modulated. When we compare the maximum value of the accumulated time with that of the excitation position parameters, we study the management of scalar and vector rogue waves, such as the excitations C.-Q. Dai (B)· Y.-Y. Wang (B) College of Sciences, Zhejiang A&F University, Lin’an 311300, People’s Republic of China e-mail: [email protected] Y.-Y. Wang e-mail: [email protected] C.-Q. Dai · Y.-Y. Wang Zhejiang Provincial Key Laboratory of Chemical Utilization of Forestry Biomass, Zhejiang A&F University, Lin’an 311300, Zhejiang, People’s Republic of China J.-F. Zhang School of Electronics Information, Zhejiang University of Media and Communications, Hangzhou 310018, People’s Republic of China
of full shape, early shape and climax shape for rogue waves. Keywords Scalar and vector rogue waves · Nonautonomous-coupled nonlinear Schrödinger equation · Partial nonlocality · Projecting expression
1 Introduction Nonlinear waves exist in various context of engineering and physics, such as mathematical physics [1–3], fluids [4–6], optics [7,8], etc. The research on diversified localized modes of nonlinear Schrödinger (NLS)like equations has been made important advances [9– 11]. Based on the NLS-like equation, enormous localized modes were reported [12–14]. The NLS-like equation with the variation of nonlinearity and dispersion was called nonautonomous one [15]. Higher dimensional solitons [16,17], rogue wave [18], vortex [19] and ring soliton [20] of nonautonomous NLS-like equations were taken shape. These structures can explain some specific issues and be potentially applied in BECs and nonlinear optics. Rogue waves as extreme wave events are being aroused widespread concern [21,22]. They portray events with high amplitude and are considered as “invisible events” with appearing and disappearing randomly and untraceably in various research fields [23]. This label has been applied to describe oceanic expanses [24], pulses emerging in optical fibres [25],
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and waves in Bose-Einstein condensates [26], atmosphere [27], plasma [28] and even in finance [29]. The NLS-like equation
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