In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order...In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order of solutions of the equation.展开更多
The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation...The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known resulr of the integrable Ablowitz-Ladik system.展开更多
In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
We report the existence of chirped bright and dark solitons for higher order nonlinear Schrodinger equation in the presence of localized dissipation. The parameter domains are delineated in which these solitons exist....We report the existence of chirped bright and dark solitons for higher order nonlinear Schrodinger equation in the presence of localized dissipation. The parameter domains are delineated in which these solitons exist. It is found that the chirp associated with each of the soliton pulses is directly proportional to intensity and gets saturated at some finite value as the retarded time approaches its asymptotic value. We further show that the higher order nonlinearities in the system such as self-steepening and self-frequency shift do not influence the amplitude of the soliton pulses significantly but primarily control the strength of the localized dissipation.展开更多
In this paper, we investigate the complex oscillation of higher order homogenous and non- homogeneous linear differential equations with meromorphic coefficients of iterated order, and obtain some results which improv...In this paper, we investigate the complex oscillation of higher order homogenous and non- homogeneous linear differential equations with meromorphic coefficients of iterated order, and obtain some results which improve and extend those given by Z. X. Chen, L. Kinnunen, etc.展开更多
In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule o...In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters a and ;3 which denote the contribution of the higher-order terms （dispersions and nonlinear effects） included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.展开更多
In birefringent optical fibers, the propagation of femtosecond soliton pulses is described by coupled higherorder nonlinear Schrodinger equations. In this paper, we will investigate the bright and dark soliton solutio...In birefringent optical fibers, the propagation of femtosecond soliton pulses is described by coupled higherorder nonlinear Schrodinger equations. In this paper, we will investigate the bright and dark soliton solutions of（2＋1）-dimensional coupled higher-order nonlinear Schrodinger equations, with the aid of symbolic computation and the Hirota method. On the basis of soliton solutions, we test and discuss the interactions graphically between the solitons in the x-z, x-t, and z-t planes.展开更多
In this paper,the rogue waves of the higher-order dispersive nonlinear Schrdinger(HDNLS) equation are investigated,which describes the propagation of ultrashort optical pulse in optical fibers.The rogue wave solutions...In this paper,the rogue waves of the higher-order dispersive nonlinear Schrdinger(HDNLS) equation are investigated,which describes the propagation of ultrashort optical pulse in optical fibers.The rogue wave solutions of HDNLS equation are constructed by using the modified Darboux transformation method.The explicit first and secondorder rogue wave solutions are presented under the plane wave seeding solution background.The nonlinear dynamics and properties of rogue waves are discussed by analyzing the obtained rational solutions.The influence of little perturbation on the rogue waves is discussed with the help of graphical simulation.展开更多
A coupled variable-coefficient higher-order nonlinear Schrodinger equation in birefringent fiber is studied, and analytical multi-solton, combined bright and dark soliton, W-shaped and M-shaped soliton solutions are o...A coupled variable-coefficient higher-order nonlinear Schrodinger equation in birefringent fiber is studied, and analytical multi-solton, combined bright and dark soliton, W-shaped and M-shaped soliton solutions are obtained. Nonlinear tunnelling of these combined solitons in dispersion barrier and dispersion well on an exponential background is discussed, and the decaying or increasing, even lossless tunnelling behaviors of combined solitons are decided by the decaying or increasing parameter.展开更多
We derive the Lax pairs and integrability conditions of the nonlinear Schrdinger equation with higher-order terms, complex potentials, and time-dependent coefficients. Cubic and quintic nonlinearities together with de...We derive the Lax pairs and integrability conditions of the nonlinear Schrdinger equation with higher-order terms, complex potentials, and time-dependent coefficients. Cubic and quintic nonlinearities together with derivative terms are considered. The Lax pairs and integrability conditions for some of the well-known nonlinear Schrdinger equations, including a new equation which was not considered previously in the literature, are then derived as special cases. We show most clearly with a similarity transformation that the higher-order terms restrict the integrability to linear potential in contrast with quadratic potential for the standard nonlinear Schrdinger equation.展开更多
文摘In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order of solutions of the equation.
基金The project partially supported by the Research Grants Council under Grant Nos, HKU 7123/05E and HKU 7184/04E
文摘The Hirota equation is a higher order extension of the nonlinear Schr6dinger equation by incorporating third order dispersion and one form of self steepening effect, New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete periodic patterns reproduces the known resulr of the integrable Ablowitz-Ladik system.
文摘In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
文摘We report the existence of chirped bright and dark solitons for higher order nonlinear Schrodinger equation in the presence of localized dissipation. The parameter domains are delineated in which these solitons exist. It is found that the chirp associated with each of the soliton pulses is directly proportional to intensity and gets saturated at some finite value as the retarded time approaches its asymptotic value. We further show that the higher order nonlinearities in the system such as self-steepening and self-frequency shift do not influence the amplitude of the soliton pulses significantly but primarily control the strength of the localized dissipation.
基金This research is supported by the Research Foundation of Doctor Points of China （No. 20060422049） and the National Natural Science Foundation of China （No. 10371065）.
文摘In this paper, we investigate the complex oscillation of higher order homogenous and non- homogeneous linear differential equations with meromorphic coefficients of iterated order, and obtain some results which improve and extend those given by Z. X. Chen, L. Kinnunen, etc.
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In this paper, we provide determinant representation of the n-th order rogue wave solutions for a higherorder nonlinear Schr6dinger equation （HONLS） by the Darboux transformation and confirm the decomposition rule of the rogue wave solutions up to fourth-order. These solutions have two parameters a and ;3 which denote the contribution of the higher-order terms （dispersions and nonlinear effects） included in the HONLS equation. Two localized properties, i.e., length and width of the first-order rogue wave solution are expressed by above two parameters, which show analytically a remarkable influence of higher-order terms on the rogue wave. Moreover, profiles of the higher-order rogue wave solutions demonstrate graphically a strong compression effect along t-direction given by higher-order terms.
基金Supported by the National Natural Science Foundation of China under Grant No.61671227the Natural Science Foundation of Shandong Province under Grant No.ZR2014AM018
文摘In birefringent optical fibers, the propagation of femtosecond soliton pulses is described by coupled higherorder nonlinear Schrodinger equations. In this paper, we will investigate the bright and dark soliton solutions of（2＋1）-dimensional coupled higher-order nonlinear Schrodinger equations, with the aid of symbolic computation and the Hirota method. On the basis of soliton solutions, we test and discuss the interactions graphically between the solitons in the x-z, x-t, and z-t planes.
基金Supported by the National Natural Science Foundation of China under Grant No.11071164Innovation Program of Shanghai Municipal Education Commission under Grant Nos.12YZ105 and 13ZZ118+1 种基金the Foundation of University Young Teachers Training Program of Shanghai Municipal Education Commission under Grant No.slg11029the National Natural Science Foundation of China under Grant No.11171220
文摘In this paper,the rogue waves of the higher-order dispersive nonlinear Schrdinger(HDNLS) equation are investigated,which describes the propagation of ultrashort optical pulse in optical fibers.The rogue wave solutions of HDNLS equation are constructed by using the modified Darboux transformation method.The explicit first and secondorder rogue wave solutions are presented under the plane wave seeding solution background.The nonlinear dynamics and properties of rogue waves are discussed by analyzing the obtained rational solutions.The influence of little perturbation on the rogue waves is discussed with the help of graphical simulation.
基金Supported by the Scientific Research Fund of Zhejiang Provincial Education Department under Grant No.Y201120994the Zhejiang Provincial Natural Science Foundation of China under Grant No.LY13A05001
文摘A coupled variable-coefficient higher-order nonlinear Schrodinger equation in birefringent fiber is studied, and analytical multi-solton, combined bright and dark soliton, W-shaped and M-shaped soliton solutions are obtained. Nonlinear tunnelling of these combined solitons in dispersion barrier and dispersion well on an exponential background is discussed, and the decaying or increasing, even lossless tunnelling behaviors of combined solitons are decided by the decaying or increasing parameter.
基金the support provided by United Arab Emirates University under the NRF grantthe support provided by King Fahd University of Petroleum and Minerals under group project nos.RG1107-1,RG1107-2,RG1214-1,and RG1214-2
文摘We derive the Lax pairs and integrability conditions of the nonlinear Schrdinger equation with higher-order terms, complex potentials, and time-dependent coefficients. Cubic and quintic nonlinearities together with derivative terms are considered. The Lax pairs and integrability conditions for some of the well-known nonlinear Schrdinger equations, including a new equation which was not considered previously in the literature, are then derived as special cases. We show most clearly with a similarity transformation that the higher-order terms restrict the integrability to linear potential in contrast with quadratic potential for the standard nonlinear Schrdinger equation.
