Based on the generalized bilinear method, diversity of exact solutions of the (3 + 1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation is successfully derived by using symbolic computation with Maple. These...Based on the generalized bilinear method, diversity of exact solutions of the (3 + 1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation is successfully derived by using symbolic computation with Maple. These new solutions, named three-wave solutions and periodic wave have greatly enriched the existing literature. Via the three-dimensional images, density images and contour plots, the physical characteristics of these waves are well described. The new three-wave solutions and periodic solitary wave solutions obtained in this paper, will have a wide range of applications in the fields of physics and mechanics.展开更多
The potential for nonlinear conversion between two laser pulses in a three-level V-type medium with assistance of an auxiliary microwave resonant radiation is studied. The results show that microwave driven field can ...The potential for nonlinear conversion between two laser pulses in a three-level V-type medium with assistance of an auxiliary microwave resonant radiation is studied. The results show that microwave driven field can lead to the parametric generation of a new laser pulse with high conversion efficieney when a weak pump laser pulse is applied.展开更多
In this paper. the coupling equations describing nonlinear three-wave interaction amongRossby waves including the forcing of an external vorticity source are obtained. Under certainconditions, the coupling equations w...In this paper. the coupling equations describing nonlinear three-wave interaction amongRossby waves including the forcing of an external vorticity source are obtained. Under certainconditions, the coupling equations with a constant amplitude forcing, the stability analysis indicates that when the amplitude of the external forcing increases to a certain extent, a pitchforkbifurcation occurs. Also. it is shown fi-o m numerical results that the bifurcation can lead to chaoticbehavior of' strange' attractor. For the obtained three-variable equation, when the amplitude ofmodulated external forcing gradually increases, a Period-doubling bifurcation is found to lead tochaotic behavior. Thus, in a nonlinear three-wave coupling model in the large-scale forcedbarotropic atmospheric flow, chaotic behavior can be observed. This chaotic behavior can explainin part 30-60-day low-flequency oscillations observed in mid-high latitudes.展开更多
We investigate the three-wave resonant interaction (TWRI) of Bogoliubov excitations in a disk-shaped Bose-Einstein condensate with the diffraction of the excitations taken into account. We show that the phase-matching...We investigate the three-wave resonant interaction (TWRI) of Bogoliubov excitations in a disk-shaped Bose-Einstein condensate with the diffraction of the excitations taken into account. We show that the phase-matching condition for the TWRI can be satisfied by a suitable selection of the wavevectors and the frequencies of the three exciting modes involved in the TWRI. Using a method of multiple-scales we derive a set of nonlinearly coupled envelope equations describing the TWRI process and give some explicit solitary-wave solutions.展开更多
We generalize the■-dressing method to investigate a(2+1)-dimensional lattice,which can be regarded as a forced(2+1)-dimensional discrete three-wave equation.The soliton solutions to the(2+1)-dimensional lattice are g...We generalize the■-dressing method to investigate a(2+1)-dimensional lattice,which can be regarded as a forced(2+1)-dimensional discrete three-wave equation.The soliton solutions to the(2+1)-dimensional lattice are given through constructing different symmetry conditions.The asymptotic analysis of one-soliton solution is discussed.For the soliton solution,the forces are zero.展开更多
Ⅰ. INTRODUCTION The model of three-wave interaction plays an important role in plasma physics and nonlinear optics. Its classical cases and quantum cases have been studied by many authors. As shown in [4], the quantu...Ⅰ. INTRODUCTION The model of three-wave interaction plays an important role in plasma physics and nonlinear optics. Its classical cases and quantum cases have been studied by many authors. As shown in [4], the quantum model is relevant to Lee model.展开更多
Recently, a considerable interest has been aroused in the study of completely integrable systems. As is well known, the dassical and quantum Yang-Baxter equations (CYBE and QYBE, respectively) play a central role in t...Recently, a considerable interest has been aroused in the study of completely integrable systems. As is well known, the dassical and quantum Yang-Baxter equations (CYBE and QYBE, respectively) play a central role in the theory of classical and quantum integrable systems. In 1973, Gaudin introduced a new class of completely integrable展开更多
Developing natural “free space” frequency upconversion is essential for photonic integrated circuits. In a singlecrystal lithium niobate thin film planar waveguide of less than 1 μm thickness, we achieve type I and...Developing natural “free space” frequency upconversion is essential for photonic integrated circuits. In a singlecrystal lithium niobate thin film planar waveguide of less than 1 μm thickness, we achieve type I and type II mode phase-matching conditions simultaneously for this thin film planar waveguide. Finally, by employing the mode phase matching of e t e → e with d_（33） at 1018 nm, we successfully achieve a green second-harmonic wave output with the conversion efficiency of 0.12%∕（W·cm^2）, which verifies one of our simulation results. The rich mode phase matching for three-wave mixing in a thin film planar waveguide may provide a potential application in on-chip frequency upconversions for integrated photonic and quantum devices.展开更多
This paper introduces an extension of the time-splitting spectral(TSSP)method for solving a general model of three-wave optical interactions,which typically arises from nonlinear optics,when the transmission media has...This paper introduces an extension of the time-splitting spectral(TSSP)method for solving a general model of three-wave optical interactions,which typically arises from nonlinear optics,when the transmission media has competing quadratic and cubic nonlinearities.The key idea is to formulate the terms related to quadratic and cubic nonlinearities into a Hermitian matrix in a proper way,which allows us to develop an explicit and unconditionally stable numerical method for the problem.Furthermore,the method is spectral accurate in transverse coordinates and second-order accurate in propagation direction,is time reversible and time transverse invariant,and conserves the total wave energy(or power or the norm of the solutions)in discretized level.Numerical examples are presented to demonstrate the efficiency and high resolution of the method.Finally the method is applied to study dynamics and interactions between three-wave solitons and continuous waves in media with competing quadratic and cubic nonlinearities in one dimension(1D)and 2D.展开更多
文摘Based on the generalized bilinear method, diversity of exact solutions of the (3 + 1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation is successfully derived by using symbolic computation with Maple. These new solutions, named three-wave solutions and periodic wave have greatly enriched the existing literature. Via the three-dimensional images, density images and contour plots, the physical characteristics of these waves are well described. The new three-wave solutions and periodic solitary wave solutions obtained in this paper, will have a wide range of applications in the fields of physics and mechanics.
基金Project supported in part by the National Natural Science Foundation of China （Grant Nos 60478029 and 10575040）.
文摘The potential for nonlinear conversion between two laser pulses in a three-level V-type medium with assistance of an auxiliary microwave resonant radiation is studied. The results show that microwave driven field can lead to the parametric generation of a new laser pulse with high conversion efficieney when a weak pump laser pulse is applied.
文摘In this paper. the coupling equations describing nonlinear three-wave interaction amongRossby waves including the forcing of an external vorticity source are obtained. Under certainconditions, the coupling equations with a constant amplitude forcing, the stability analysis indicates that when the amplitude of the external forcing increases to a certain extent, a pitchforkbifurcation occurs. Also. it is shown fi-o m numerical results that the bifurcation can lead to chaoticbehavior of' strange' attractor. For the obtained three-variable equation, when the amplitude ofmodulated external forcing gradually increases, a Period-doubling bifurcation is found to lead tochaotic behavior. Thus, in a nonlinear three-wave coupling model in the large-scale forcedbarotropic atmospheric flow, chaotic behavior can be observed. This chaotic behavior can explainin part 30-60-day low-flequency oscillations observed in mid-high latitudes.
文摘We investigate the three-wave resonant interaction (TWRI) of Bogoliubov excitations in a disk-shaped Bose-Einstein condensate with the diffraction of the excitations taken into account. We show that the phase-matching condition for the TWRI can be satisfied by a suitable selection of the wavevectors and the frequencies of the three exciting modes involved in the TWRI. Using a method of multiple-scales we derive a set of nonlinearly coupled envelope equations describing the TWRI process and give some explicit solitary-wave solutions.
基金Project 11471295 was supported by the National Natural Science Foundation of Chinapartially supported by the President’s Endowed Professorship program of the University of Texas system.
文摘We generalize the■-dressing method to investigate a(2+1)-dimensional lattice,which can be regarded as a forced(2+1)-dimensional discrete three-wave equation.The soliton solutions to the(2+1)-dimensional lattice are given through constructing different symmetry conditions.The asymptotic analysis of one-soliton solution is discussed.For the soliton solution,the forces are zero.
文摘Ⅰ. INTRODUCTION The model of three-wave interaction plays an important role in plasma physics and nonlinear optics. Its classical cases and quantum cases have been studied by many authors. As shown in [4], the quantum model is relevant to Lee model.
文摘Recently, a considerable interest has been aroused in the study of completely integrable systems. As is well known, the dassical and quantum Yang-Baxter equations (CYBE and QYBE, respectively) play a central role in the theory of classical and quantum integrable systems. In 1973, Gaudin introduced a new class of completely integrable
基金supported by the National Natural Science Foundation of China under Grant Nos.11574208 and61235009
文摘Developing natural “free space” frequency upconversion is essential for photonic integrated circuits. In a singlecrystal lithium niobate thin film planar waveguide of less than 1 μm thickness, we achieve type I and type II mode phase-matching conditions simultaneously for this thin film planar waveguide. Finally, by employing the mode phase matching of e t e → e with d_（33） at 1018 nm, we successfully achieve a green second-harmonic wave output with the conversion efficiency of 0.12%∕（W·cm^2）, which verifies one of our simulation results. The rich mode phase matching for three-wave mixing in a thin film planar waveguide may provide a potential application in on-chip frequency upconversions for integrated photonic and quantum devices.
基金support from the National University of Singapore grant No.R-146-000-081-112C.Zheng acknowledges the support by National Natural Science Foundation of China(No.10401020)his extended visit at National University of Singapore.
文摘This paper introduces an extension of the time-splitting spectral(TSSP)method for solving a general model of three-wave optical interactions,which typically arises from nonlinear optics,when the transmission media has competing quadratic and cubic nonlinearities.The key idea is to formulate the terms related to quadratic and cubic nonlinearities into a Hermitian matrix in a proper way,which allows us to develop an explicit and unconditionally stable numerical method for the problem.Furthermore,the method is spectral accurate in transverse coordinates and second-order accurate in propagation direction,is time reversible and time transverse invariant,and conserves the total wave energy(or power or the norm of the solutions)in discretized level.Numerical examples are presented to demonstrate the efficiency and high resolution of the method.Finally the method is applied to study dynamics and interactions between three-wave solitons and continuous waves in media with competing quadratic and cubic nonlinearities in one dimension(1D)and 2D.
