Finite-dimensional integrable Hamiltonian systems, obtained through the non- linearization of the 3×3 spectral problems associated with the Manakov and the derivative Manakov equations, are investigated. A genera...Finite-dimensional integrable Hamiltonian systems, obtained through the non- linearization of the 3×3 spectral problems associated with the Manakov and the derivative Manakov equations, are investigated. A generating function method is used to give a simple and effective way to prove the involutivity of integrals. Finite-parameter solutions of the Manakov and the derivative Manakov equations are calculated based on the commutative systems of ordinary differential equations with these integrals as Hamiltonians.展开更多
In the field of maritime transport,motion and energy,the dynamics of deep-sea waves is one of the major problems in ocean science.A mathematical modeling of dynamics of solitary waves in deep sea under the two-layer s...In the field of maritime transport,motion and energy,the dynamics of deep-sea waves is one of the major problems in ocean science.A mathematical modeling of dynamics of solitary waves in deep sea under the two-layer stratification leads to NLS equation,and consequently,the interaction two of them can be formulated by coupled NLS equation.In this work,extended auxiliary equation and the exp(−ω(χ))-expansion methods are employed to make the optical solutions of the Manakov model of coupled NLS equation.The methods used in this paper,in addition to providing the analysis of individual wave solutions,also provide general optical solutions.Some previously known solutions can be obtained by some special selections of parameters obtained by solving systems of algebraic equations.At this stage,it is more practical and convenient to apply methods with a symbolic calculation system.展开更多
It is well-known that the general Manakov system is a 2-components nonlinear Schrodinger equation with 4 nonzero real parameters.The analytic property of the general Manakov system has been well-understood though it l...It is well-known that the general Manakov system is a 2-components nonlinear Schrodinger equation with 4 nonzero real parameters.The analytic property of the general Manakov system has been well-understood though it looks complicated.This paper devotes to exploring geometric properties of this system via the prescribed curvature representation in the category of Yang-Mills’theory.Three models of moving curves evolving in the symmetric Lie algebras u(2,1)=k_(α)⊕m_(α)(α=1,2)and u(3)=k_(3)⊕m_(3)are shown to be simultaneously the geometric realization of the general Manakov system.This reflects a new phenomenon in geometric realization of a partial differential equation/system.展开更多
In the biased guest-host photorefractive polymer, the Manakov equations can be used to describe the op- tical soliton propagation and interaction. Hereby for such equations, via the Hirota method and syrnbolic computa...In the biased guest-host photorefractive polymer, the Manakov equations can be used to describe the op- tical soliton propagation and interaction. Hereby for such equations, via the Hirota method and syrnbolic computation, analytic soliton solutions in the bright-dark and dark-dark forms are obtained. Based on the choice of photorefrac- rive polymer parameter and incident-optical-beam parameter, the bright-dark and dark-dark solitons as well as their interaction can occur in the polymer when the total intensity is much lower than the background illumination, and our analysis indicates that the incident light with different polarization directions influence little on the soliton propagation. ~, representing the soliton intensity far away from the soliton center, determines the appearance of bright or dark soliton under the background illumination. Through the graphic and asymptotic analysis on the two-soliton solutions along with the different ~, we find that there exist the elastic and inelastic interactions between the bright-dark solitons, while the interactions between the dark-dark solitons are always elastic.展开更多
It is shown that bright-dark Manakov solitons can be formed in biased guest-host photorefractive polymer when the total intensity of two components is much lower than the background illumination. The existing conditio...It is shown that bright-dark Manakov solitons can be formed in biased guest-host photorefractive polymer when the total intensity of two components is much lower than the background illumination. The existing conditions of bright-dark Manakov solitons are discussed in detail. The intensity profiles and dynamical evolutions of solitons are presented by numericaJ methods.展开更多
Modulation instabilities in the randomly birefringent two-mode optical fibers （RB-TMFs） are analyzed in detail by accounting the effects of the differential mode group delay （DMGD） and group velocity dispersion （...Modulation instabilities in the randomly birefringent two-mode optical fibers （RB-TMFs） are analyzed in detail by accounting the effects of the differential mode group delay （DMGD） and group velocity dispersion （GVD） ratio between the two modes, both of which are absent in the randomly birefringent single-mode optical fibers （RB-SMFs）. New MI characteristics are found in both normal and anomalous dispersion regimes. For the normal dispersion, without DMGD, no MI exists. With DMGD, a completely new MI band is generated as long as the total power is smaller than a critical total power value, named by Per, which increases significantly with the increment of DMGD, and reduces dramatically as GVD ratio and power ratio between the two modes increases. For the anomalous dispersion, there is one MI band without DMGD. In the presence of DMGD, the MI gain is reduced generally. On the other hand, there also exists a critical total power （Per）, which increases （decreases） distinctly with the increment of DMGD （GVD ratio of the two modes） but varies complicatedly with the power ratio between the two modes. Two MI bands are present for total power smaller than Per, and the dominant band can be switched between the low and high frequency bands by adjusting the power ratio between the two modes. The M1 analysis in this paper is verified by numerical simulation.展开更多
基金Supported by the Special Funds for Major State Basic Research Project of China(G20000077301)
文摘Finite-dimensional integrable Hamiltonian systems, obtained through the non- linearization of the 3×3 spectral problems associated with the Manakov and the derivative Manakov equations, are investigated. A generating function method is used to give a simple and effective way to prove the involutivity of integrals. Finite-parameter solutions of the Manakov and the derivative Manakov equations are calculated based on the commutative systems of ordinary differential equations with these integrals as Hamiltonians.
文摘In the field of maritime transport,motion and energy,the dynamics of deep-sea waves is one of the major problems in ocean science.A mathematical modeling of dynamics of solitary waves in deep sea under the two-layer stratification leads to NLS equation,and consequently,the interaction two of them can be formulated by coupled NLS equation.In this work,extended auxiliary equation and the exp(−ω(χ))-expansion methods are employed to make the optical solutions of the Manakov model of coupled NLS equation.The methods used in this paper,in addition to providing the analysis of individual wave solutions,also provide general optical solutions.Some previously known solutions can be obtained by some special selections of parameters obtained by solving systems of algebraic equations.At this stage,it is more practical and convenient to apply methods with a symbolic calculation system.
基金supported by the National Natural Science Foundation of China(Nos.12071080,12141104)the Science Technology Project of Jiangxi Educational Committee(No.GJJ2201202)the Natural Science Foundation of Jiangxi Province(Nos.20212BAB211005,20232BAB201006)。
文摘It is well-known that the general Manakov system is a 2-components nonlinear Schrodinger equation with 4 nonzero real parameters.The analytic property of the general Manakov system has been well-understood though it looks complicated.This paper devotes to exploring geometric properties of this system via the prescribed curvature representation in the category of Yang-Mills’theory.Three models of moving curves evolving in the symmetric Lie algebras u(2,1)=k_(α)⊕m_(α)(α=1,2)and u(3)=k_(3)⊕m_(3)are shown to be simultaneously the geometric realization of the general Manakov system.This reflects a new phenomenon in geometric realization of a partial differential equation/system.
基金Supported by the National Natural Science Foundation of China under Grant No.11272023the Open Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications)Supported by the Fundamental Research Funds for the Central Universities of China under Grant No.2011BUPTYB02
文摘In the biased guest-host photorefractive polymer, the Manakov equations can be used to describe the op- tical soliton propagation and interaction. Hereby for such equations, via the Hirota method and syrnbolic computation, analytic soliton solutions in the bright-dark and dark-dark forms are obtained. Based on the choice of photorefrac- rive polymer parameter and incident-optical-beam parameter, the bright-dark and dark-dark solitons as well as their interaction can occur in the polymer when the total intensity is much lower than the background illumination, and our analysis indicates that the incident light with different polarization directions influence little on the soliton propagation. ~, representing the soliton intensity far away from the soliton center, determines the appearance of bright or dark soliton under the background illumination. Through the graphic and asymptotic analysis on the two-soliton solutions along with the different ~, we find that there exist the elastic and inelastic interactions between the bright-dark solitons, while the interactions between the dark-dark solitons are always elastic.
基金Supported by the Natural Science Foundation of Shanxi Province under Grant No. 2011011003-2the Science and Technology Development Foundation of Higher Education of Shanxi Province under Grant No. 20111125
文摘It is shown that bright-dark Manakov solitons can be formed in biased guest-host photorefractive polymer when the total intensity of two components is much lower than the background illumination. The existing conditions of bright-dark Manakov solitons are discussed in detail. The intensity profiles and dynamical evolutions of solitons are presented by numericaJ methods.
基金Project supported by the Natural Science Foundation of Jiangsu Provincial Universities(Grant No.14KJB140009)the National Natural Science Foundation of China(Grant No.11447113)the Startup Foundation for Introducing Talent of NUIST(Grant No.2241131301064)
文摘Modulation instabilities in the randomly birefringent two-mode optical fibers （RB-TMFs） are analyzed in detail by accounting the effects of the differential mode group delay （DMGD） and group velocity dispersion （GVD） ratio between the two modes, both of which are absent in the randomly birefringent single-mode optical fibers （RB-SMFs）. New MI characteristics are found in both normal and anomalous dispersion regimes. For the normal dispersion, without DMGD, no MI exists. With DMGD, a completely new MI band is generated as long as the total power is smaller than a critical total power value, named by Per, which increases significantly with the increment of DMGD, and reduces dramatically as GVD ratio and power ratio between the two modes increases. For the anomalous dispersion, there is one MI band without DMGD. In the presence of DMGD, the MI gain is reduced generally. On the other hand, there also exists a critical total power （Per）, which increases （decreases） distinctly with the increment of DMGD （GVD ratio of the two modes） but varies complicatedly with the power ratio between the two modes. Two MI bands are present for total power smaller than Per, and the dominant band can be switched between the low and high frequency bands by adjusting the power ratio between the two modes. The M1 analysis in this paper is verified by numerical simulation.
