A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such no...A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such nonlinear wave equations admit richer classical and nonclassical symmetries, leading to the conservation laws and the reduction of the wave equations. Some exact solutions of the considered wave equations for particular cases are derived.展开更多
The transient surface wave motion is studied by a method which transfers the computational re- gion into a unit circle. In place of the Green's formula of harmonic function the Taylor's series of an analyti- c...The transient surface wave motion is studied by a method which transfers the computational re- gion into a unit circle. In place of the Green's formula of harmonic function the Taylor's series of an analyti- cal function is used. The coefficients of the series are determined by FFT. The numerical filtration is accomplished in the Fourier domain.展开更多
In this paper we study one-dimensional Fisher-Kolmogorov equation with density dependent non-linear diffusion. We choose the diffusion as a function of cell density such that it is high in highly cell populated areas ...In this paper we study one-dimensional Fisher-Kolmogorov equation with density dependent non-linear diffusion. We choose the diffusion as a function of cell density such that it is high in highly cell populated areas and it is small in the regions of fewer cells. The Fisher equation with non-linear diffusion is known as modified Fisher equation. We study the travelling wave solution of modified Fisher equation and find the approximation of minimum wave speed analytically, by using the eigenvalues of the stationary states, and numerically by using COMSOL (a commercial finite element solver). The results reveal that the minimum wave speed depends on the parameter values involved in the model. We observe that when diffusion is moderately non-linear, the eigenvalue method correctly predicts the minimum wave speed in our numerical calculations, but when diffusion is strongly non-linear the eigenvalues method gives the wrong answer.展开更多
The characteristic of combustion wave and its change were analyzed by numerical value calculation and computer simulation, based on the combustion dynamical model of SHS process. It is shown that with the change of co...The characteristic of combustion wave and its change were analyzed by numerical value calculation and computer simulation, based on the combustion dynamical model of SHS process. It is shown that with the change of condition parameters in SHS process various time-space order combustion waves appear. It is concluded from non-liner dynamical mechanism analysis that the strong coupling of two non-linear dynamical processes is the dynamical mechanism causing the time-space order dissipation structures.展开更多
In this paper, the time-dependent invariant of the Dirac equation with time-dependent linear potential has been constructed in non-commutative phase space. The corresponding analytical solution of the Dirac equation i...In this paper, the time-dependent invariant of the Dirac equation with time-dependent linear potential has been constructed in non-commutative phase space. The corresponding analytical solution of the Dirac equation is presented by Lewis-Riesenfield invariant method.展开更多
Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers syst...Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers system is derived.展开更多
An efficient widely tunable terahertz（THz）-wave parametric oscillator （TPO） has been designed based on the basic principle of optical parametric oscillator. The design of TPO comprises the theoretical calculations...An efficient widely tunable terahertz（THz）-wave parametric oscillator （TPO） has been designed based on the basic principle of optical parametric oscillator. The design of TPO comprises the theoretical calculations for wavelength dependent refractive index dependent wavelength when the frequency is in the far infrared region, the low-loss parametric gain has been discussed as a same form as the parametric gain in the optical region, realized the non-collinear phase-matching conditions of the terahertz optical parametric oscillator and structure of lithium niobate （LiNbO3） for TPO. The tunable spectrum range of terahertz-wave has been achieved. To increase THz output, a cut exit was made at the comer of the LiNbO3 crystal.展开更多
A new method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension. The nonlinear surface is expressed by Fourie...A new method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension. The nonlinear surface is expressed by Fourier series with finite number of terms, after the computational domain is transformed into a unit circle. The dynamic boundary equation is used in its exact nonlinear form and the coefficients of Fourier series are found by the Newton-Raphson method successively. This is a neat method, Yielding high prescision with little computational effort.展开更多
In order to suppress the error induced by the modified differential equations, a compensative proce- dure is designed to desoribe the higher order effect of the non-linear interaction of the solitary waves.
With an analysis of zonal wind observations over 40 years, Salby and Callaghan [1] showed that the Quasi-biennial Oscillation (QBO) at 20 km is modulated by 11-year solar cycle (SC) variations from about 12 to 20 m/s ...With an analysis of zonal wind observations over 40 years, Salby and Callaghan [1] showed that the Quasi-biennial Oscillation (QBO) at 20 km is modulated by 11-year solar cycle (SC) variations from about 12 to 20 m/s (Figure 2). The observations are reproduced qualitatively in a study with the 3D Numerical Spectral Model, which shows that the SC effect of the stratospheric QBO is produced by dynamical downward coupling originating in the mesosphere. In this modeling study, the SC period is taken to be 10 years, and a realistic heat source is applied varying exponentially with altitude: 0.2%, surface;2%, 50 km;20%, 100 km and above. The numerical results show that the variable solar radiation in the mesosphere around 65 km generates a hemispheric symmetric Equatorial Annual Oscillation (EAO), which is modulated by relatively large SC variations. Under the influence of wave mean flow interactions, the EAO propagates into the lower atmosphere and is the dynamical source or pacemaker for the large SC modulation of the QBO. The numerical results show that the upward propagating small-scale gravity waves from the troposphere amplify the SC modulations of the QBO and EAO in the stratosphere, part of the SC mechanism. The zonal winds of the equatorial QBO and EAO produce through the meridional circulation measurable SC variations in the temperature of the stratosphere and troposphere at high latitudes. Analysis of NCEP temperature and zonal wind data (1958 to 2006) provides observational evidence of the EAO with SC variations around 11 years.展开更多
Based upon the perturbation method,this paper used the method of conformal mapping to solve the deformation and breaking of nonlinear waves in water of gradually varying depth.The wave characteristics,such as wave def...Based upon the perturbation method,this paper used the method of conformal mapping to solve the deformation and breaking of nonlinear waves in water of gradually varying depth.The wave characteristics,such as wave deformation,velocity field,breaker type and breaker height are discussed by the third order approximation.Results obtained are compared with experimental data.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11071159 and11301259)the Shanghai Key Projects(No.12510501700)+1 种基金the Scientific Research of College of Inner Mongolia(No.NJZZ14053)the Natural Science Foundation of Inner Mongolia(Nos.2013MS0105and 2014MS0114)
文摘A complete classical symmetry classification and a nonclassical symmetry classification of a class of nonlinear wave equations are given with three arbitrary parameter functions. The obtained results show that such nonlinear wave equations admit richer classical and nonclassical symmetries, leading to the conservation laws and the reduction of the wave equations. Some exact solutions of the considered wave equations for particular cases are derived.
基金The project supported by National Natural Science Foundation of China
文摘The transient surface wave motion is studied by a method which transfers the computational re- gion into a unit circle. In place of the Green's formula of harmonic function the Taylor's series of an analyti- cal function is used. The coefficients of the series are determined by FFT. The numerical filtration is accomplished in the Fourier domain.
文摘In this paper we study one-dimensional Fisher-Kolmogorov equation with density dependent non-linear diffusion. We choose the diffusion as a function of cell density such that it is high in highly cell populated areas and it is small in the regions of fewer cells. The Fisher equation with non-linear diffusion is known as modified Fisher equation. We study the travelling wave solution of modified Fisher equation and find the approximation of minimum wave speed analytically, by using the eigenvalues of the stationary states, and numerically by using COMSOL (a commercial finite element solver). The results reveal that the minimum wave speed depends on the parameter values involved in the model. We observe that when diffusion is moderately non-linear, the eigenvalue method correctly predicts the minimum wave speed in our numerical calculations, but when diffusion is strongly non-linear the eigenvalues method gives the wrong answer.
基金Funded by the National Natural Science Foundation of Chi-na(50062001)
文摘The characteristic of combustion wave and its change were analyzed by numerical value calculation and computer simulation, based on the combustion dynamical model of SHS process. It is shown that with the change of condition parameters in SHS process various time-space order combustion waves appear. It is concluded from non-liner dynamical mechanism analysis that the strong coupling of two non-linear dynamical processes is the dynamical mechanism causing the time-space order dissipation structures.
文摘In this paper, the time-dependent invariant of the Dirac equation with time-dependent linear potential has been constructed in non-commutative phase space. The corresponding analytical solution of the Dirac equation is presented by Lewis-Riesenfield invariant method.
文摘Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers system is derived.
文摘An efficient widely tunable terahertz（THz）-wave parametric oscillator （TPO） has been designed based on the basic principle of optical parametric oscillator. The design of TPO comprises the theoretical calculations for wavelength dependent refractive index dependent wavelength when the frequency is in the far infrared region, the low-loss parametric gain has been discussed as a same form as the parametric gain in the optical region, realized the non-collinear phase-matching conditions of the terahertz optical parametric oscillator and structure of lithium niobate （LiNbO3） for TPO. The tunable spectrum range of terahertz-wave has been achieved. To increase THz output, a cut exit was made at the comer of the LiNbO3 crystal.
文摘A new method is presented for the computation of two-dimensional periodic progressive surface waves propagating under the combined influence of gravity and surface tension. The nonlinear surface is expressed by Fourier series with finite number of terms, after the computational domain is transformed into a unit circle. The dynamic boundary equation is used in its exact nonlinear form and the coefficients of Fourier series are found by the Newton-Raphson method successively. This is a neat method, Yielding high prescision with little computational effort.
基金The project supported by National Natural Science Foundation of China
文摘In order to suppress the error induced by the modified differential equations, a compensative proce- dure is designed to desoribe the higher order effect of the non-linear interaction of the solitary waves.
文摘With an analysis of zonal wind observations over 40 years, Salby and Callaghan [1] showed that the Quasi-biennial Oscillation (QBO) at 20 km is modulated by 11-year solar cycle (SC) variations from about 12 to 20 m/s (Figure 2). The observations are reproduced qualitatively in a study with the 3D Numerical Spectral Model, which shows that the SC effect of the stratospheric QBO is produced by dynamical downward coupling originating in the mesosphere. In this modeling study, the SC period is taken to be 10 years, and a realistic heat source is applied varying exponentially with altitude: 0.2%, surface;2%, 50 km;20%, 100 km and above. The numerical results show that the variable solar radiation in the mesosphere around 65 km generates a hemispheric symmetric Equatorial Annual Oscillation (EAO), which is modulated by relatively large SC variations. Under the influence of wave mean flow interactions, the EAO propagates into the lower atmosphere and is the dynamical source or pacemaker for the large SC modulation of the QBO. The numerical results show that the upward propagating small-scale gravity waves from the troposphere amplify the SC modulations of the QBO and EAO in the stratosphere, part of the SC mechanism. The zonal winds of the equatorial QBO and EAO produce through the meridional circulation measurable SC variations in the temperature of the stratosphere and troposphere at high latitudes. Analysis of NCEP temperature and zonal wind data (1958 to 2006) provides observational evidence of the EAO with SC variations around 11 years.
文摘Based upon the perturbation method,this paper used the method of conformal mapping to solve the deformation and breaking of nonlinear waves in water of gradually varying depth.The wave characteristics,such as wave deformation,velocity field,breaker type and breaker height are discussed by the third order approximation.Results obtained are compared with experimental data.
