Vector breathers, rogue and breather-rogue waves for a coupled mixed derivative nonlinear Schrödinger system in an optical fiber

Gao, Yi–Tian; Yu, Xin; Li, Liu-Qing; Ding, Chaoliang

doi:10.1007/s11071-022-08058-2

Cited by 58 publications

(11 citation statements)

References 57 publications

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“…( ) ˆ( ), a variable-coefficient generalized Korteweg-de Vries model with dissipative, perturbed and external-force terms for the pulse waves in a blood vessel or dynamics in a circulatory system [17] (and references therein) r r h r h By the bye, more nonlinear evolution equations might be found, for instance, in [24][25][26][27][28].…”

Section: ˜˜˜˜( ) ˜˜( ) ( )mentioning

confidence: 99%

Theoretical investigations on a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers model for a dilated artery, blood vessel or circulatory system with experimental support

Gao

Guo

Shan

2023

Commun. Theor. Phys.

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Recent theoretical-physics efforts have been focused on the probes for nonlinear pulse waves in the variable-radius arteries. With respect to the nonlinear waves in an artery full of blood with certain aneurysm, pulses in a blood vessel or features in a circulatory system, this paper symbolically computes out an auto-Backlund transformation via a noncharacteristic movable singular manifold, certain families of the solitonic solutions as well as a family of the similarity reductions for a variable-coefficient generalized forced-perturbed Korteweg-de Vries-Burgers equation. Aiming, e.g., at the dynamical radial displacement superimposed on the original static deformation from an arterial wall, our results rely on the axial stretch of the injured artery, blood as an incompressible Newtonian fluid, radius variation along the axial direction or aneurysmal geometry, viscosity of the fluid, thickness of the artery, mass density of the membrane material, mass density of the fluid, strain energy density of the artery, shear modulus, stretch ratio, etc. We also call the attention that the shock-wave structures from our solutions agree well with those dusty-plasma-experimentally reported.

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Section: ˜˜˜˜( ) ˜˜( ) ( )mentioning

confidence: 99%

Theoretical investigations on a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers model for a dilated artery, blood vessel or circulatory system with experimental support

Gao

Guo

Shan

2023

Commun. Theor. Phys.

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“…( 13) and (14). Their parameters, i.e., their amplitudes A 1 and A 2 , their (common) width b, and their internal frequencies ν 1 and ν 2 are related through simple mathematical expressions to the coefficients P j and Q i j of the CNLS equations ( 13) and (14). Each component of these vector solitons represent modulated electrostatic wavepackets which are moving in the plasma and interact strongly and nonlinearly with strengths Q 12 and Q 21 .…”

Section: Modulational Instability: Compatibility Condition and Growth...mentioning

confidence: 99%

“…A pair of nonlinearly coupled nonlinear Schrödinger equations (hereafter referred to as the CNLS system of equations) arises as a prototype model of mathematical physics, which occurs in various physical contexts [1][2][3][4] , including water waves 5,6 , left-handed (negative refraction index) transmission lines 7 , optical pulse propagation in birefringence fibers 8,9 , and in optical nonlinear media 10 , vector solitons in left-handed metamaterials 11 , polarized pulse pair propagation in anisotropic dispersive media 12 , pulse propagation in isotropic Kerr media with chromatic dispersion 13 , and even breathers and rogue waves in optical fibers 14 . 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] .…”

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

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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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“…1. More symbolic-computation studies have been reported, e.g., in Wu and Gao (2023), Gao et al (2022c) and Wu et al (2023a).…”

Section: Notesmentioning

confidence: 99%

Letter to the Editor: Thinking of the oceanic shallow water in the light of a (2+1)-dimensional generalized dispersive long-wave system related to HFF 33, 3272; 33, 965 and 32, 2282

Gao

2023

HFF

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Recently, in International Journal of Numerical Methods for Heat and Fluid Flow, Liu (2023), Khuri (2023) andLi et al. (2022) have done some excellent work on the oceanic shallow water, respectively, via a (3þ1)-dimensional generalized shallow water wave equation in an ocean or simulating the weather, a (2þ1)-dimensional Korteweg-de Vries equation for the shallow water waves and a (2þ1)-dimensional Broer-Kaup-Kupershmidt system modeling the nonlinear and dispersive long gravity waves in the shallow water of uniform depth.Getting enthusiastic from Liu (2023), Khuri ( 2023) and Li et al. (2022), this Letter designs to symbolically compute a (2þ1)-dimensional generalized dispersive long-wave system modeling certain dispersive and nonlinear long gravity waves in two directions, horizontally, on the shallow water of an ocean (Gao et al., 2022b(Gao et al., , 2023a(Gao et al., , 2021b(Gao et al., , 2021c(Gao et al., , 2020, i.e.:Letter to the Editor 3801

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Vector breathers, rogue and breather-rogue waves for a coupled mixed derivative nonlinear Schrödinger system in an optical fiber

Cited by 58 publications

References 57 publications

Theoretical investigations on a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers model for a dilated artery, blood vessel or circulatory system with experimental support

Theoretical investigations on a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers model for a dilated artery, blood vessel or circulatory system with experimental support

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

Letter to the Editor: Thinking of the oceanic shallow water in the light of a (2+1)-dimensional generalized dispersive long-wave system related to HFF 33, 3272; 33, 965 and 32, 2282

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