L-A pairs with rational dependence on spectral parameters. Darboux transformation

1989 ◽  
Vol 46 (5) ◽  
pp. 2094-2096
Author(s):  
M. A. Sall'
Keyword(s):  
Darboux Transformation ◽  
Spectral Parameters ◽  
Rational Dependence

Generalized Darboux transformation and asymptotic analysis on the degenerate dark-bright solitons for a coupled nonlinear Schrödinger system

2021 ◽  
Author(s):  
He-yuan Tian ◽  
Bo Tian ◽  
Yan Sun ◽  
Su-Su Chen
Keyword(s):  
Asymptotic Analysis ◽  
Darboux Transformation ◽  
Coupled System ◽  
Bound State ◽  
Bright Soliton ◽  
Spectral Parameters ◽  
Nonlinear Superposition ◽  
Bright Solitons ◽  
Generalized Darboux Transformation ◽  
The Given

Abstract In this paper, our work is based on a coupled nonlinear Schr ̈odinger system in a two-mode nonlinear fiber. A (N,m)-generalized Darboux transformation is constructed to derive the Nth-order solutions, where the positive integers N and m denote the numbers of iterative times and of distinct spectral parameters, respectively. Based on the Nth-order solutions and the given steps to perform the asymptotic analysis, it is found that a degenerate dark-bright soliton is the nonlinear superposition of several asymptotic dark-bright solitons possessing the same profile. For those asymptotic dark-bright solitons, their velocities are z-dependent except that one of those velocities could become z-independent under the certain condition, where z denotes the evolution dimension. Those asymptotic dark-bright solitons are reflected during the interaction. When a degenerate dark-bright soliton interacts with a nondegenerate/degenerate dark-bright soliton, the interaction is elastic, and the asymptotic bound-state dark-bright soliton with z-dependent or z-independent velocity could take place under certain conditions. Our study extends the investigation on the degenerate solitons from the bright soliton case for the scalar equations to the dark-bright soliton case for a coupled system.

Novel localized wave interaction phenomena and dynamics in the generalized discrete Hirota equation via the generalized (2,N − 2)-fold Darboux transformation

2019 ◽  
Vol 33 (17) ◽  
pp. 1950192 ◽  
Author(s):  
Hao-Tian Wang ◽  
Xiao-Yong Wen ◽  
Yaqing Liu
Keyword(s):  
Darboux Transformation ◽  
Wave Interaction ◽  
Inelastic Interaction ◽  
Discrete Version ◽  
The Novel ◽  
Spectral Parameters ◽  
Small Noise ◽  
Hirota Equation ◽  
Interaction Solutions ◽  
Dynamical Behaviors

We investigate the generalized discrete Hirota equation, which is an integrable discrete version of Hirota equation. The generalized [Formula: see text]-fold Darboux transformation (i.e. generalized [Formula: see text]-fold Darboux transformation when [Formula: see text] with two spectral parameters) is presented to derive the novel localized wave interaction solutions. Moreover, some inelastic interaction evolution phenomena of rogue wave and breather are studied graphically. Numerical simulations are used to explore the dynamical behaviors of certain localized wave interaction solutions, which show that their evolutions are stable against a small noise. The results obtained in this paper can be used to find the interaction properties of localized nonlinear waves in nonlinear optics and relevant fields.

Darboux transformation and solitons for an integrable nonautonomous nonlinear integro-differential Schrödinger equation

2017 ◽  
Vol 31 (30) ◽  
pp. 1750276 ◽  
Author(s):  
Xuelin Yong ◽  
Yajing Fan ◽  
Yehui Huang ◽  
Wen-Xiu Ma ◽  
Jing Tian
Keyword(s):  
Schrödinger Equation ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Variable Coefficients ◽  
Spectral Parameters ◽  
Solitonic Excitations ◽  
Isospectral Problem ◽  
Soliton Management

By modifying the scheme for an isospectral problem, the non-isospectral Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy is constructed via allowing the time varying spectrum. In this paper, we consider an integrable nonautonomous nonlinear integro-differential Schrödinger equation discussed before in “Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation” [Y. J. Zhang, D. Zhao and H. G. Luo, Ann. Phys. 350 (2014) 112]. We first analyze the integrability conditions and identify the model. Second, we modify the existing Darboux transformation (DT) for such a non-isospectral problem. Third, the nonautonomous soliton solutions are obtained via the resulting DT and basic properties of these solutions in the inhomogeneous media are discussed graphically to illustrate the influences of the variable coefficients. In the process, a technique by selecting appropriate spectral parameters instead of the variable inhomogeneities is employed to realize a different type of one-soliton management. Several novel optical solitons are constructed and their features are shown by some specific figures. In addition, four kinds of the special localized two-soliton solutions are obtained. The solitonic excitations localized both in space and time, which exhibit the feature of the so-called rogue waves but with a zero background, are discussed.

Global explicit solutions with n double spectral parameters for the Myrzakulov-I equation

2016 ◽  
Vol 30 (29) ◽  
pp. 1650358 ◽  
Author(s):  
Hai Chen ◽  
Zi-Xiang Zhou
Keyword(s):  
Darboux Transformation ◽  
Explicit Solutions ◽  
Spectral Parameters

The Darboux transformation with n double spectral parameters for the Myrzakulov-I equation is obtained by taking suitable limit of the spectral parameters. Global explicit solutions are obtained by using this Darboux transformation with n double spectral parameters.

Effect of amiodarone on heart rate variability in patients with newly diagnosed atrial fibrillation (clinical observation)

2020 ◽  
pp. 81-85
Author(s):  
E. P. Popova ◽  
O. T. Bogova ◽  
S. N. Puzin ◽  
D. A. Sychyov ◽  
V. P. Fisenko
Keyword(s):  
Atrial Fibrillation ◽  
Heart Rate ◽  
Heart Rate Variability ◽  
Drug Therapy ◽  
Heart Function ◽  
Newly Diagnosed ◽  
Class Iii ◽  
Spectral Parameters ◽  
Patient Will ◽  
The Individual

Spectral analysis of heart rate variability gives an idea of the role of the autonomic nervous system in the regulation of chronotropic heart function. This method can be used to evaluate the effectiveness of drug therapy. Drug therapy should be carried out taking into account the individual clinical form of atrial fibrillation. Information about the vegetative status of the patient will undoubtedly increase the effectiveness of treatment. In this study, spectral parameters were studied in patients with newly diagnosed atrial fibrillation. The effect of antiarrhythmic drug class III amiodarone on the spectral parameters of heart rate variability was studied.

ESTIMATION OF SPECTRAL PARAMETERS OF SCATTERED SIGNALS IN RADARS OF VERTICAL SOUNDING OF THE ATMOSPHERE

2018 ◽  
Vol 77 (3) ◽  
pp. 187-198
Author(s):  
V. N. Oleynikov ◽  
S. V. Doroshenko ◽  
V. D. Pshenichny
Keyword(s):  
Spectral Parameters
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