The breather and semi-rational rogue wave solutions for the coupled mixed derivative nonlinear Schrödinger equations

Jin, Jie; Zhang, Yi; Ye, Rusuo; Wu, Lifei

doi:10.1007/s11071-022-07834-4

Cited by 5 publications

(3 citation statements)

References 33 publications

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“…For BB, BD, DB and DD vector solitons to exist in the CNLS system that we have obtain from the particular plasma fluid model considered here, the right-hand-sides of Eqs. ( 24), ( 30), (34), and (38), respectively, must be greater than zero (so that A 2 and b are real; A 1 is of course fixed to a real number). This condition for the existence of the four types of vector solitons can be expressed simply as α < 0, β < 0, Case I, BB vector solitons, (40) α > 0, β < 0, Case II, BD vector solitons, (41) α > 0, β > 0, Case III, DB vector solitons, (42) α < 0, β > 0, Case IV, DD vector solitons .…”

Section: /19mentioning

confidence: 99%

“…Formally similar systems of equations have been used to model light (beam) propagation [15][16][17][18] and electrostatic or electromagnetic wave propagation in plasmas [19][20][21][22][23][24][25][26] . Independently from a physical context, various studies of vector solitons and rogue waves have been carried out, based on general CNLS models 6,[27][28][29][30][31][32] , and variants of CNLS equations such as coupled derivative nonlinear Schrödinger equations 33,34 , vector (N−component) CNLS [35][36][37] , nonlocal CNLS 38 , CNLS equations with variable coefficients 39 , coherently coupled CNLS equations 40 , and coupled high-order nonlinear Schrödinger equations 41 , among others, have been investigated with respect to vector solitons and rogue waves.…”

Section: Introductionmentioning

confidence: 99%

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Electrostatic wave interaction via asymmetric vector solitons as precursor to rogue wave formation in non-Maxwellian plasmas

Lazarides

Veldes

Frantzeskakis

et al. 2023

Preprint

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An asymmetric pair of coupled nonlinear Schrödinger (CNLS) equations has been derived through a multiscale perturbation method applied to a plasma fluid model, in which two wavepackets of distinct (carrier) wavenumbers (k1 and k2) and amplitudes (Ψ1 and Ψ2) are allowed to co-propagate and interact. The original fluid model was set up for a non-magnetized plasma consisting of cold inertial ions evolving against a κ−distributed electron background in one dimension. The reduction procedure resulting in the CNLS equations has provided analytical expressions for the dispersion, self-modulation and cross-coupling coefficients in terms of the two carrier wavenumbers. These coefficients present no symmetry whatsoever, in the general case (of different wavenumbers). The possibility for coupled envelope (vector soliton) solutions to occur has been investigated. Although the CNLS equations are asymmetric and non-integrable, in principle, the system admits various types of vector soliton solutions, physically representing nonlinear, localized electrostatic plasma modes, whose areas of existence is calculated on the wavenumbers’ parameter plane. The possibility for either bright (B) or dark (D) type excitations for either of the (2) waves provides four (4) combinations for the envelope pair (BB, BD, DB, DD), if a set of explicit criteria is satisfied. Moreover, the soliton parameters (maximum amplitude, width) are also calculated for each type of vector soliton solution, in its respective area of existence. The dependence of the vector soliton characteristics on the (two) carrier wavenumbers and on the spectral index κ characterizing the electron distribution has been explored. In certain cases, the (envelope) amplitude of one component may exceed its counterpart (second amplitude) by a factor 2.5 or higher, indicating that rogue waves (freak waves) may be formed due to modulational interactions among copropagating wavepackets. As κ decreases from large values, modulational instability occurs in larger areas of the parameter plane(s) and with higher growth rates. The distribution of different types of vector solitons on the parameter plane(s) also varies significantly with decreasing κ, and in fact dramatically for κ between 3 and 2. Deviation from the Maxwell-Boltzmann picture therefore seems to favor modulational instability as a precursor to the formation of bright (predominantly) type envelope excitations and freak waves.

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Section: /19mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Electrostatic wave interaction via asymmetric vector solitons as precursor to rogue wave formation in non-Maxwellian plasmas

Lazarides

Veldes

Frantzeskakis

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Electron plasma (Langmuir) waves and ion acoustic waves [24,25,26], amidst other studies that focused mostly on electromagnetic modes [27,28,29,30,31,32,33]. Beyond plasma science, general forms of CNLS equations have been investigated in recent years with respect to the existence of vector solitons, breathers, and rogue wave solutions, in contexts including higher-order coupled NLS systems [34,35], coupled mixed-derivative NLS equations [36,37,38], variable coefficients CNLS equations [39], non-autonomous CNLS equations [40,41,42], systems involving four-wave mixing terms [43], coupled cubic-quintic NLS equations [44], space-shifted CNLS equations [45] and non-autonomous partially non-local CNLS equations [46], among others.…”

Section: Introductionmentioning

confidence: 99%

Coupled Nonlinear Schrodinger (CNLS) Equations for two interacting electrostatic wavepackets in a non-Maxwellian fluid plasma model

Lazarides

Kourakis

2023

Preprint

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The nonlinear dynamics of two co-propagating electrostatic wavepackets in a one-dimensional non-magnetized plasma fluid model is considered, from first principles. The coupled waves are characterized by different (carrier) wavenumbers and amplitudes. A plasma consisting of non-thermalized (κ−distributed) electrons evolving against a cold (stationary) ion background is considered. The original model is reduced, by means of a multiple-scale perturbation method, to a pair of coupled nonlinear Schr¨odinger (CNLS) equations for the dynamics of the wavepacket envelopes. For arbitrary wavenumbers, the resulting CNLS equations exhibit no known symmetry and thus intrinsically differ from the Manakov system, in general. Exact analytical expressions have been derived for the dispersion, self-modulation (nonlinearity) and cross-modulation (coupling) coefficients involved in the CNLS equations, as functions of the wavenumbers (k1, k2) and of the spectral index κ characterizing the electron profile. An analytical investigation has thus been carried out of the modulational instability (MI) properties of this pair of wavepackets, focusing on the role of the intrinsic (variable) parameters. Modulational instability is shown to occur in most parts of the parameter space. The instability window(s) and the corresponding growth rate are calculated numerically in a number of case studies. Two-wave interaction favors MI by extending its range of occurrence and by enhancing its growth rate. Growth rate patterns obtained for different κ index (values) suggest that deviation from thermal (Maxwellian) equilibrium, for low κ values, leads to enhances MI of the interacting wave pair. Although we have focused on electrostatic wavepacket propagation in nonthermal (non-Maxwellian) plasma, the results of this study are generic and may be used as basis to model energy localization in nonlinear optics, in hydrodynamics or in dispersive media with Kerr-type nonlinearities where modulational instability is relevant.

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Coupled nonlinear Schrödinger (CNLS) equations for two interacting electrostatic wavepackets in a non-Maxwellian fluid plasma model

Lazarides,

Kourakis

2023

Nonlinear Dyn

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The nonlinear dynamics of two co-propagating electrostatic wavepackets in a one-dimensional non-magnetized plasma fluid model is considered, from first principles. The coupled waves are characterized by different (carrier) wavenumbers and amplitudes. A plasma consisting of non-thermalized ($$\kappa $$ κ -distributed) electrons evolving against a cold (stationary) ion background is considered. The original model is reduced, by means of a multiple-scale perturbation method, to a pair of coupled nonlinear Schrödinger (CNLS) equations for the dynamics of the wavepacket envelopes. For arbitrary wavenumbers, the resulting CNLS equations exhibit no known symmetry and thus intrinsically differ from the Manakov system, in general. Exact analytical expressions have been derived for the dispersion, self-modulation (nonlinearity) and cross-modulation (coupling) coefficients involved in the CNLS equations, as functions of the wavenumbers ($$k_1$$ k 1 , $$k_2$$ k 2 ) and of the spectral index $$\kappa $$ κ characterizing the electron profile. An analytical investigation has thus been carried out of the modulational instability (MI) properties of this pair of wavepackets, focusing on the role of the intrinsic (variable) parameters. Modulational instability is shown to occur in most parts of the parameter space. The instability window(s) and the corresponding growth rate are calculated numerically in a number of case studies. Two-wave interaction favors MI by extending its range of occurrence and by enhancing its growth rate. Growth rate patterns obtained for different $$\kappa $$ κ index (values) suggest that deviation from thermal (Maxwellian) equilibrium, for low $$\kappa $$ κ values, leads to enhance MI of the interacting wave pair. To the best of our knowledge, the dynamics of two co-propagating wavepackets in a plasma described by a fluid model with $$\kappa $$ κ -distributed electrons is investigated thoroughly with respect to their MI properties as a function of $$\kappa $$ κ for the first time, in the framework of an asymmetric CNLS system whose coefficients present no obvious symmetries for arbitrary $$k_1$$ k 1 and $$k_2$$ k 2 . Although we have focused on electrostatic wavepacket propagation in non-thermal (non-Maxwellian) plasma, the results of this study are generic and may be used as basis to model energy localization in nonlinear optics, in hydrodynamics or in dispersive media with Kerr-type nonlinearities where MI is relevant.

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The breather and semi-rational rogue wave solutions for the coupled mixed derivative nonlinear Schrödinger equations

Cited by 5 publications

References 33 publications

Electrostatic wave interaction via asymmetric vector solitons as precursor to rogue wave formation in non-Maxwellian plasmas

Electrostatic wave interaction via asymmetric vector solitons as precursor to rogue wave formation in non-Maxwellian plasmas

Coupled Nonlinear Schrodinger (CNLS) Equations for two interacting electrostatic wavepackets in a non-Maxwellian fluid plasma model

Coupled nonlinear Schrödinger (CNLS) equations for two interacting electrostatic wavepackets in a non-Maxwellian fluid plasma model

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