The periodic solution to Nino-Southern the model for the El oscillation

A class of oscillator of the EI Nifio-Southern oscillation model is considered. Using Mawhin＇s continuation theorem, a result on the existence of periodic solutions for ENSO model is obtained.     

Singularly perturbed solution of a sea--air oscillator model for the ENSO

A time delay equation for the sea--air oscillator model is studied. The aim is to create an asymptotic solving method of nonlinear equation for the El Ni\tilde{\rm n}o--Southern Oscillation model. And based on a class of oscillators of the model, employing the method of ENSO singular perturbation, the asymptotic solution of corresponding problem is obtained. It is proven from the results that the method of singular perturbation can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific of the atmosphere--ocean oscillation for ENSO model.     

The periodic solution to the model for the El Nio-Southern oscillation

A class of oscillator of the El Ni?o-Southern oscillation model is considered. Using Mawhin's continuation theorem, a result on the existence of periodic solutions for ENSO model is obtained.     

The homotopic method of travelling wave solution for El Nino tropic sea-air coupled oscillator

The EI Nimo and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. In this paper, an asymptotic method of solving nonlinear equations for the ENSO model is proposed. And based on a class of oscillator of the ENSO model and by employing the method of homotopic mapping, the approximate solution of equations for the corresponding ENSO model is studied. It is proved from the results that homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for the ENSO model.     

Asymptotic solution for the El Nino time delay sea-air oscillator model

A sea-air oscillator model is studied using the time delay theory. The aim is to find an asymptotic solving method for the El Nino-southern oscillation （ENSO） model. Employing the perturbed method, an asymptotic solution of the corresponding problem is obtained. Thus we can obtain the prognoses of the sea surface temperature （SST） anomaly and the related physical quantities.     

The homotopic mapping method for sea-air oscillator model of interdecadal climate fluctuations

The E1 Nifio/La Nifia Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a coupled system of sea-air oscillator model is studied. The aim is to create an asymptotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the method of homotopic mapping, the approximate solution of corresponding problem is studied. It is proven from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.     

Perturbation method of studying the EI Nifio oscillation with two parameters by using the delay sea-air oscillator model

The EI Nio-southern oscillation (ENSO) is an interannual phenomenon involved in tropical Pacific oceanatmosphere interactions. In this paper, we develop an asymptotic method of solving the nonlinear equation using the ENSO model. Based on a class of the oscillator of the ENSO model, a approximate solution of the corresponding problem is studied employing the perturbation method.     

Asymptotic solution of a sea--air oscillator for ENSO mechanism

The EI Ni\~{n}o/La Ni\~{n}a--Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific ocean--atmosphere interactions. In this paper, a class of coupled system of the ENSO mechanism is considered. Based on a class of oscillator of ENSO model, the asymptotic solution of a corresponding problem is studied by employing the approximate method. It is proved from the results that the perturbation method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere--ocean oscillation for the ENSO model.     

Asymptotic solution for the El Nio time delay sea-air oscillator model

A sea-air oscillator model is studied using the time delay theory.The aim is to find an asymptotic solving method for the El Nio -southern oscillation (ENSO) model.Employing the perturbed method,an asymptotic solution of the corresponding problem is obtained.Thus we can obtain the prognoses of the sea surface temperature (SST) anomaly and the related physical quantities.     

Asymptotic solution for the El Ni no time delay seaben air oscillator model

A sea—air oscillator model is studied using the time delay theory. The aim is to find an asymptotic solving method for the El Ni no-southern oscillation (ENSO) model. Employing the perturbed method, an asymptotic solution of the corresponding problem is obtained. Thus we can obtain the prognoses of the sea surface temperature (SST) anomaly and the related physical quantities.     

The periodic solution to a delayed sea-air oscillator coupling model for the El Nifio-Southern Oscillation （ENSO）

A time-delay sea-air oscillator coupling model is studied. Using Mawhin＇s continuation theorem, the result on the existence of periodic solutions for the sea-air oscillator model is obtained.     

Homotopic method of solving a class of EI Nino/La Nina-Southern Oscillation sea-air oscillator

The EI Nino/La Nina-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Ocean-atmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is created. And based on a class of oscillator of the ENSO model, the approximate solution of a corresponding problem is studied by employing the method of homotopic mapping. It is proved from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for the ENSO model.     

Asymptotic solving method for sea-air coupled oscillator ENSO model

The ENSO is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interaction.In this article,we create an asymptotic solving method for the nonlinear system of the ENSO model.The asymptotic solution is obtained.And then we can furnish weather forecasts theoretically and other behaviors and rules for the atmosphere-ocean oscillator of the ENSO.     

Asymptotic solution for a class of sea-air oscillator model for El Nin^～o-southern oscillation

The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.     

Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species.     

Variational iteration method for solving the mechanism of the Equatorial Eastern Pacific El Nino-Southern Oscillation

A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.     

Homotopic mapping solution of an oscillator for the El Nino / La Nina-southern oscillation

This paper considers a class of oscillator for the El Nin o/La Nin a-southern oscillation (ENSO) model.By using the homotopic mapping method,it obtains approximations of the solution for the ENSO model.     

Comparison Between the Full Quantum Dynamics and the Quantum—Semiclassical Models to Many—Particle Systems

We consider a simple collinear collision of a “classical“ particle with a harmonic oscillator within quantumsemiclassical model and full quantum dynamics model,in which the latter is solved analytically in squeezed state and exact diagonalization methods and acts as the exact solution of such a system.A comparison of these two models for different mass ratios between the “classical“ particle and the quantum particle is done,which gives a criterion when using the quantum-semiclassical model.     

The sea--air oscillator model of decadal variations in subtropical cells and equatorial Pacific SST

In this paper a time delay equation for sea--air oscillator model is studied. The aim is to create an approximate solving method of nonlinear equation for sea--air oscillator model. Employing the method of variational iteration, it obtains the approximate solution of corresponding equation. This method is an approximate analytic method, which can be often used for analysing other behaviour of the sea surface temperature anomaly of the atmosphere--ocean oscillator model.     

Numerical simulation and experimental validation of a direct current air corona discharge under atmospheric pressure

Air corona discharge is one of the critical problems associated with high-voltage equipment. Investigating the corona mechanism plays a key role in enhancing the electrical insulation performance. An improved self-consistent multi-component two-dimensional plasma hybrid model is presented for the simulation of a direct current atmospheric pressure corona discharge in air. The model is based on plasma hydrodynamic and chemical models, and includes 12 species and 26 reactions. In addition, the photoionization effect is introduced into the model. The simulation on a bar-plate electrode configuration with an inter-electrode gap of 5.0 mm is carried out. The discharge voltage-current characteristics and the current density distribution predicted by the hybrid model agree with the experimental measurements. In addition, the dynamics of volume charged species generation, discharge current waveform, current density distribution at an electrode, charge density, electron temperature, and electric field variations are investigated in detail based on the model. The results indicate that the model can contribute valuable insights into the physics of an air plasma discharge.