Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generali...Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.展开更多
By considering higher-order effects, the properties of self-similar parabolic pulses propagating in the microstructured fibre amplifier with a normal group-velocity dispersion have been investigated. The numerical res...By considering higher-order effects, the properties of self-similar parabolic pulses propagating in the microstructured fibre amplifier with a normal group-velocity dispersion have been investigated. The numerical results indicate that the higher-order effects can badly distort self-similar parabolic pulse shape and optical spectrum, and at the same time the peak shift and oscillation appear, while the pulse still reveals highly linear chirp but grows into asymmetry. The influence of different higher-order effects on self-similar parabolic pulse propagation has been analysed. It shows that the self-steepening plays a more important role. We can manipulate the geometrical parameters of the microstructured fibre amplifier to gain a suitable dispersion and nonlinearity coefficient which will keep high-quality self-similar parabolic pulse propagation. These results are significant for the further study of self-similar parabolic pulse propagation.展开更多
We analytically study optical rogue waves in the presence of quintic nonlinearity and nonlinear dispersion effects. Dynamics of the rogue waves are investigated through the precise expressions of their peak, valley, t...We analytically study optical rogue waves in the presence of quintic nonlinearity and nonlinear dispersion effects. Dynamics of the rogue waves are investigated through the precise expressions of their peak, valley, trajectory,and width. Based on this, the properties of a few specific rogue waves are demonstrated in detail, and the dynamical evolution of rogue waves can be well controlled under different nonlinearity management. It shows that the peak reaches its maximum and the valley becomes minimized when the width evolves to the minimum value. Moreover, we find that the higher-order effects here achieve balance due to the integrability, and they only influence the rogue waves' trajectory.展开更多
The nonlinear theory of interaction between the q analogue of a single-mode field and a Ξ-type threelevel atom has been established. And the formal solution of the Schrodinger equation in the representation and its a...The nonlinear theory of interaction between the q analogue of a single-mode field and a Ξ-type threelevel atom has been established. And the formal solution of the Schrodinger equation in the representation and its average number are obtained. Then, the photon squeezing effects are studied through numerical calculation. The results show that the q deformation nonlinear action has a lot of influence on the quantum coherence and quantum properties. When q approaches 1, the theory reduces to the common linear theory.展开更多
The interaction between three optical solitons is a complex and valuable research direction,which is of practical application for promoting the development of optical communication and all-optical information processi...The interaction between three optical solitons is a complex and valuable research direction,which is of practical application for promoting the development of optical communication and all-optical information processing technology.In this paper,we start from the study of the variable-coefficient coupled higher-order nonlinear Schodinger equation(VCHNLSE),and obtain an analytical three-soliton solution of this equation.Based on the obtained solution,the interaction of the three optical solitons is explored when they are incident from different initial velocities and phases.When the higher-order dispersion and nonlinear functions are sinusoidal,hyperbolic secant,and hyperbolic tangent functions,the transmission properties of three optical solitons before and after interactions are discussed.Besides,this paper achieves effective regulation of amplitude and velocity of optical solitons as well as of the local state of interaction process,and interaction-free transmission of the three optical solitons is obtained with a small spacing.The relevant conclusions of the paper are of great significance in promoting the development of high-speed and large-capacity optical communication,optical signal processing,and optical computing.展开更多
Acoustic nonlinearity holds potential as a method for assessing material stress.Analogous to the acoustoelastic effect,where the velocity of elastic waves is influenced by third-order elastic constants,the propagation...Acoustic nonlinearity holds potential as a method for assessing material stress.Analogous to the acoustoelastic effect,where the velocity of elastic waves is influenced by third-order elastic constants,the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants.Despite this,there has been a notable absence of research exploring this phenomenon.Consequently,this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials.It delves into the impact of pre-stress on higher-order material parameters,and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress.This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials.展开更多
The paper discusses on the quantum fundamental soliton states in the frame of the quantum noalinear Schrodinger equation, calculates position and momentum fluctuations,and analyzes the squeezing effect of photon numbe...The paper discusses on the quantum fundamental soliton states in the frame of the quantum noalinear Schrodinger equation, calculates position and momentum fluctuations,and analyzes the squeezing effect of photon number in the soliton states.展开更多
The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equatio...The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equation,provide its Lax pair, and present its rational soliton solutions and self-potential function by using the degenerate Darboux transformation. From the numerical plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution produced by δ are discussed.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.12271096)the Natural Science Foundation of Fujian Province(Grant No.2021J01302)。
文摘Under investigation is the n-component nonlinear Schrödinger equation with higher-order effects,which describes the ultrashort pulses in the birefringent fiber.Based on the Lax pair,the eigenfunction and generalized Darboux transformation are derived.Next,we construct several novel higher-order localized waves and classified them into three categories:(i)higher-order rogue waves interacting with bright/antidark breathers,(ii)higher-order breather fission/fusion,(iii)higherorder breather interacting with soliton.Moreover,we explore the effects of parameters on the structure,collision process and energy distribution of localized waves and these characteristics are significantly different from previous ones.Finally,the dynamical properties of these solutions are discussed in detail.
基金Project supported by the National Science Foundation of Guangdong Province,China(Grant No04010397)
文摘By considering higher-order effects, the properties of self-similar parabolic pulses propagating in the microstructured fibre amplifier with a normal group-velocity dispersion have been investigated. The numerical results indicate that the higher-order effects can badly distort self-similar parabolic pulse shape and optical spectrum, and at the same time the peak shift and oscillation appear, while the pulse still reveals highly linear chirp but grows into asymmetry. The influence of different higher-order effects on self-similar parabolic pulse propagation has been analysed. It shows that the self-steepening plays a more important role. We can manipulate the geometrical parameters of the microstructured fibre amplifier to gain a suitable dispersion and nonlinearity coefficient which will keep high-quality self-similar parabolic pulse propagation. These results are significant for the further study of self-similar parabolic pulse propagation.
基金Supported by the National Natural Science Foundation of China(NSFC)under Grant No.11347605the Ministry of Education Doctoral Program Funds under Grant No.20126101110004
文摘We analytically study optical rogue waves in the presence of quintic nonlinearity and nonlinear dispersion effects. Dynamics of the rogue waves are investigated through the precise expressions of their peak, valley, trajectory,and width. Based on this, the properties of a few specific rogue waves are demonstrated in detail, and the dynamical evolution of rogue waves can be well controlled under different nonlinearity management. It shows that the peak reaches its maximum and the valley becomes minimized when the width evolves to the minimum value. Moreover, we find that the higher-order effects here achieve balance due to the integrability, and they only influence the rogue waves' trajectory.
文摘The nonlinear theory of interaction between the q analogue of a single-mode field and a Ξ-type threelevel atom has been established. And the formal solution of the Schrodinger equation in the representation and its average number are obtained. Then, the photon squeezing effects are studied through numerical calculation. The results show that the q deformation nonlinear action has a lot of influence on the quantum coherence and quantum properties. When q approaches 1, the theory reduces to the common linear theory.
基金supported by the Scientific Research Foundation of Weifang University of Science and Technology(Grant Nos.KJRC2022002 and KJRC2023035).
文摘The interaction between three optical solitons is a complex and valuable research direction,which is of practical application for promoting the development of optical communication and all-optical information processing technology.In this paper,we start from the study of the variable-coefficient coupled higher-order nonlinear Schodinger equation(VCHNLSE),and obtain an analytical three-soliton solution of this equation.Based on the obtained solution,the interaction of the three optical solitons is explored when they are incident from different initial velocities and phases.When the higher-order dispersion and nonlinear functions are sinusoidal,hyperbolic secant,and hyperbolic tangent functions,the transmission properties of three optical solitons before and after interactions are discussed.Besides,this paper achieves effective regulation of amplitude and velocity of optical solitons as well as of the local state of interaction process,and interaction-free transmission of the three optical solitons is obtained with a small spacing.The relevant conclusions of the paper are of great significance in promoting the development of high-speed and large-capacity optical communication,optical signal processing,and optical computing.
基金supported by the National Natural Science Foundation of China(No.12134002)。
文摘Acoustic nonlinearity holds potential as a method for assessing material stress.Analogous to the acoustoelastic effect,where the velocity of elastic waves is influenced by third-order elastic constants,the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants.Despite this,there has been a notable absence of research exploring this phenomenon.Consequently,this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials.It delves into the impact of pre-stress on higher-order material parameters,and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress.This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials.
文摘The paper discusses on the quantum fundamental soliton states in the frame of the quantum noalinear Schrodinger equation, calculates position and momentum fluctuations,and analyzes the squeezing effect of photon number in the soliton states.
基金Supported by the National Natural Science Foundation of China under Grant No.11271210the K.C.Wong Magna Fund in Ningbo University
文摘The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equation,provide its Lax pair, and present its rational soliton solutions and self-potential function by using the degenerate Darboux transformation. From the numerical plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution produced by δ are discussed.
