The cubic-quintic nonlinear Schroedinger equation （CQNLS） plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic sol...The cubic-quintic nonlinear Schroedinger equation （CQNLS） plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schroedinger equation with variable coefficients （vCQNLS） are derived with the aid of a set of subsidiary high-order ordinary differential equations （sub-equations for short）. The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.展开更多
Some new exact travelling wave and period solutions of discrete nonlinearSchroedinger equation are found by using a hyperbolic tangent function approach, which was usuallypresented to find exact travelling wave soluti...Some new exact travelling wave and period solutions of discrete nonlinearSchroedinger equation are found by using a hyperbolic tangent function approach, which was usuallypresented to find exact travelling wave solutions of certain nonlinear partial differential models.Now we can further extend the new algorithm to other nonlinear differential-different models.展开更多
We extend the method of searching “eigen-operator” of the square of the Schroedinger operator to the interaction picture, which not only helps to construct Hamiltonians of two kinds of parametric amplifiers but also...We extend the method of searching “eigen-operator” of the square of the Schroedinger operator to the interaction picture, which not only helps to construct Hamiltonians of two kinds of parametric amplifiers but also leads to a new uncertainty relation regarding to the free Hamiltonian and the interacting Hamiltonian.展开更多
An efficient scheme is proposed for the generation of atomic Schroedinger cat states in an optical cavity. In the scheme N three-level atoms are loaded in the optical cavity. Raman coupling of two ground states is ach...An efficient scheme is proposed for the generation of atomic Schroedinger cat states in an optical cavity. In the scheme N three-level atoms are loaded in the optical cavity. Raman coupling of two ground states is achieved via a laser tield and the cavity mode. The cavity mode is always in the vacuum state and the atoms have no probability of being populated in the excited state. Thus, the scheme is insensitive to both the cavity decay and spontaneous emission.展开更多
In this letter, abundant families of Jacobi elliptic function envelope solutions of the N-coupled nonlinear Schroedinger （NLS） system are obtained directly. When the modulus m → 1, those periodic solutions degenera...In this letter, abundant families of Jacobi elliptic function envelope solutions of the N-coupled nonlinear Schroedinger （NLS） system are obtained directly. When the modulus m → 1, those periodic solutions degenerate as the corresponding envelope soliton solutions, envelope shock wave solutions. Especially, for the 3-coupled NLS system, five types of Jacobi elliptic function envelope solutions are illustrated both analytically and graphically. Two types of those degenerate as envelope soliton solutions.展开更多
We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponent...We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.展开更多
In this paper, two novel semiclassical methods including the standard and supersymmetric WKB quantization conditions are suggested to discuss the Schroedinger equation with position-dependent effective mass. From a pr...In this paper, two novel semiclassical methods including the standard and supersymmetric WKB quantization conditions are suggested to discuss the Schroedinger equation with position-dependent effective mass. From a proper coordinate transformation, the formalism of the Schroedinger equation with position-dependent effective mass is mapped into isospectral one with constant mass and therefore for a given mass distribution and physical potential function the bound state energy spectrum can be determined easily by above method associated with a simple integral formula. It is shown that our method can give the analytical results for some exactly-solvable quantum systems.展开更多
In this paper, we give a simplified proof on the energy scattering for the nonlinear Schroedinger equations with interaction terems by use of the interaction Morawetz estimate, which is originally introduced in [4].
By applying Lou＇s direct perturbation method to perturbed nonlinear Schroedinger equation and the critical nonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the ...By applying Lou＇s direct perturbation method to perturbed nonlinear Schroedinger equation and the critical nonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the zero-order and the first-order solutions are obtained. Based on these approximate solutions, the analytical forms of parameters of solitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time. In addition, the perturbed nonlinear Schroedinger equations is directly simulated by split-step Fourier method to check the validity of the direct perturbation method. It turns out that the analytical results given by the direct perturbation method are well supported by numerical calculations.展开更多
We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representat...We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.展开更多
We investigate the classical dynamics of the massive SU(2) Yang-Mills field in the framework of multiple scale perturbation theory. We show analytically that there exists a subset of solutions having the form of a kin...We investigate the classical dynamics of the massive SU(2) Yang-Mills field in the framework of multiple scale perturbation theory. We show analytically that there exists a subset of solutions having the form of a kink soliton, modulated by a plane wave, in a linear subspace transverse to the direction of free propagation. Subsequently, we explore how these solutions affect the dynamics of a Dirac field possessing an SU(2) charge. We find that this class of Yang- Mills configurations, when regarded as an external field, leads to the localization of the fermion along a line in the transverse space. Our analysis reveals a mechanism for trapping SU(2) charged fermions in the presence of an external Yang-Mills field indicating the non-abelian analogue of Landau localization in electrodynamics.展开更多
In this note, we prove that the Schrodinger flow of maps from a closed Rieman surface into a compact irreducible Hermitian symmetric space admits a global weak solution. Also, we show the existence of weak solutions t...In this note, we prove that the Schrodinger flow of maps from a closed Rieman surface into a compact irreducible Hermitian symmetric space admits a global weak solution. Also, we show the existence of weak solutions to the initial value problem of Heisenberg model wit Lie algebra values, which is closely related to the Schrodinger flow on compact Hermitian symmetric spaces.展开更多
In this paper ,the existence of homoclinic orbits,for a perturbed cubic-quintic nonlinear Schroedinger equation with even periodic boundary conditions ,under the geralized parameters conditions is established.More spe...In this paper ,the existence of homoclinic orbits,for a perturbed cubic-quintic nonlinear Schroedinger equation with even periodic boundary conditions ,under the geralized parameters conditions is established.More specifically,we combine geometric singular perturbation theory,with ,Melnikov analysis and integrable theory to prove the persistences of homoclinic orbits.展开更多
In this paper,we use the Wigner meaure approach to study the semiclassical limit of nonlinear Schroedinger equation in small time.We prove that:the linits of the quantum density:ρ^ε=:|ψ^ε|^2,and the quantum moment...In this paper,we use the Wigner meaure approach to study the semiclassical limit of nonlinear Schroedinger equation in small time.We prove that:the linits of the quantum density:ρ^ε=:|ψ^ε|^2,and the quantum momentum:J^ε=:εIm(-↑ψ^ε↓△ψ^ε）satisfy the compressible Euler equations before the formation of singularities in the limit system.展开更多
Consider the blow up results for local smooth solutions of a quasilinear Schrodinger equation iut＋Δu＋β｜u｜^P-2u＋θ（Δ＋｜u｜^2）u／0,u｜t=0=u0（x）,x∈R^Nin nonisotropic space.
基金The project supported in part by Natural Science Foundation of Henan Province of China under Grant No. 2006110002 and the Science Foundation of Henan University of Science and Technology under Grant No. 2004ZD002
文摘The cubic-quintic nonlinear Schroedinger equation （CQNLS） plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schroedinger equation with variable coefficients （vCQNLS） are derived with the aid of a set of subsidiary high-order ordinary differential equations （sub-equations for short）. The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.
文摘Some new exact travelling wave and period solutions of discrete nonlinearSchroedinger equation are found by using a hyperbolic tangent function approach, which was usuallypresented to find exact travelling wave solutions of certain nonlinear partial differential models.Now we can further extend the new algorithm to other nonlinear differential-different models.
基金The project supported by National Natural Science Foundation of China and the Doctoral Tutoring Foundation of the Ministry of Education of Chin
文摘We extend the method of searching “eigen-operator” of the square of the Schroedinger operator to the interaction picture, which not only helps to construct Hamiltonians of two kinds of parametric amplifiers but also leads to a new uncertainty relation regarding to the free Hamiltonian and the interacting Hamiltonian.
文摘An efficient scheme is proposed for the generation of atomic Schroedinger cat states in an optical cavity. In the scheme N three-level atoms are loaded in the optical cavity. Raman coupling of two ground states is achieved via a laser tield and the cavity mode. The cavity mode is always in the vacuum state and the atoms have no probability of being populated in the excited state. Thus, the scheme is insensitive to both the cavity decay and spontaneous emission.
基金The project partially supported by the Foundation of Zhejiang University of Technology, the Education Foundation of Zhejiang Province of China under Grant No. 2003055, and the Foundation of Zhejiang Forestry College under Grant No. 2002FK15 Acknowledgments We would like to express our sincere thanks to the referees for useful suggestion and timely help.
文摘In this letter, abundant families of Jacobi elliptic function envelope solutions of the N-coupled nonlinear Schroedinger （NLS） system are obtained directly. When the modulus m → 1, those periodic solutions degenerate as the corresponding envelope soliton solutions, envelope shock wave solutions. Especially, for the 3-coupled NLS system, five types of Jacobi elliptic function envelope solutions are illustrated both analytically and graphically. Two types of those degenerate as envelope soliton solutions.
基金The project supported by Liu Hui Applied Mathematics Center of Nankai University and 985 Education Development Plan of Tianjin University
文摘We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three- step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.
基金The project supported by the Natural Science Foundation of Zhejiang Province of China under Grant No. Y605037 .
文摘In this paper, two novel semiclassical methods including the standard and supersymmetric WKB quantization conditions are suggested to discuss the Schroedinger equation with position-dependent effective mass. From a proper coordinate transformation, the formalism of the Schroedinger equation with position-dependent effective mass is mapped into isospectral one with constant mass and therefore for a given mass distribution and physical potential function the bound state energy spectrum can be determined easily by above method associated with a simple integral formula. It is shown that our method can give the analytical results for some exactly-solvable quantum systems.
文摘In this paper, we give a simplified proof on the energy scattering for the nonlinear Schroedinger equations with interaction terems by use of the interaction Morawetz estimate, which is originally introduced in [4].
基金The project supported by National Natural Science Foundation of China under Grant No. 10575087 and the Natural Science Foundation of Zhejiang Province of China under Grant No. 102053
文摘By applying Lou＇s direct perturbation method to perturbed nonlinear Schroedinger equation and the critical nonlinear SchrSdinger equation with a small dispersion, their approximate analytical solutions including the zero-order and the first-order solutions are obtained. Based on these approximate solutions, the analytical forms of parameters of solitons are expressed and the effects of perturbations on solitons are briefly analyzed at the same time. In addition, the perturbed nonlinear Schroedinger equations is directly simulated by split-step Fourier method to check the validity of the direct perturbation method. It turns out that the analytical results given by the direct perturbation method are well supported by numerical calculations.
文摘We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.
文摘We investigate the classical dynamics of the massive SU(2) Yang-Mills field in the framework of multiple scale perturbation theory. We show analytically that there exists a subset of solutions having the form of a kink soliton, modulated by a plane wave, in a linear subspace transverse to the direction of free propagation. Subsequently, we explore how these solutions affect the dynamics of a Dirac field possessing an SU(2) charge. We find that this class of Yang- Mills configurations, when regarded as an external field, leads to the localization of the fermion along a line in the transverse space. Our analysis reveals a mechanism for trapping SU(2) charged fermions in the presence of an external Yang-Mills field indicating the non-abelian analogue of Landau localization in electrodynamics.
文摘In this note, we prove that the Schrodinger flow of maps from a closed Rieman surface into a compact irreducible Hermitian symmetric space admits a global weak solution. Also, we show the existence of weak solutions to the initial value problem of Heisenberg model wit Lie algebra values, which is closely related to the Schrodinger flow on compact Hermitian symmetric spaces.
文摘In this paper ,the existence of homoclinic orbits,for a perturbed cubic-quintic nonlinear Schroedinger equation with even periodic boundary conditions ,under the geralized parameters conditions is established.More specifically,we combine geometric singular perturbation theory,with ,Melnikov analysis and integrable theory to prove the persistences of homoclinic orbits.
文摘In this paper,we use the Wigner meaure approach to study the semiclassical limit of nonlinear Schroedinger equation in small time.We prove that:the linits of the quantum density:ρ^ε=:|ψ^ε|^2,and the quantum momentum:J^ε=:εIm(-↑ψ^ε↓△ψ^ε）satisfy the compressible Euler equations before the formation of singularities in the limit system.
基金Supported in part by Youth Foundation of NSFC （10501006） and China Post-Doc Science Foundation.
文摘Consider the blow up results for local smooth solutions of a quasilinear Schrodinger equation iut＋Δu＋β｜u｜^P-2u＋θ（Δ＋｜u｜^2）u／0,u｜t=0=u0（x）,x∈R^Nin nonisotropic space.
