Mo Jia-Qi

A class of homotopic solving method for ENSO model

Abstract The El Nino/La Nina and the Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this article, the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models. And on the basis of a class of oscillator of ENSO models, using the method of homotopic mapping, the approximation of solution of corresponding problem is studied. It is proved from the results that homotopic method can be used for analyzing the SST anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.

Asymptotic solution for a class of sea—air oscillator model for El Niño—southern oscillation

The El Nino–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 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.

Variational iteration method for solving perturbed mechanism of western boundary undercurrents in the Pacific

A class of perturbed mechanisms for the western boundary undercurrents in the Pacific is considered. The model of generalized governing equations is studied. Employing the method of variational iteration, an approximate solution of corresponding model is obtained. It is proved from the results that the solution for the variational iteration method can be used for analysing operation of the perturbed mechanism of western boundary undercurrents in the Pacific.

Asymptotic solution of a sea–air oscillator for ENSO mechanism

The EI Nino/La Nina–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.

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 Nino–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.

A class of singularly perturbed reaction diffusion systems

A class of singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solution for the initial boundary value problems is studied.

Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation

A class of generalized complex Burgers equation is considered. First, a set of equations of the complex value functions are solved by using the homotopic mapping method. The approximate solution for the original generalized complex Burgers equation is obtained. This method can find the approximation of arbitrary order of precision simply and reliably.

The homotopic method of travelling wave solution for El Niño tropic sea–air coupled oscillator

The EI Nino 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.

The solvability for a class of singularly perturbed quasi-linear differential system

Abstract The solvability for a class of singularly perturbed Robin problem of quasi-linear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using the theory of differential inequality the uniform validity of the asymptotic expansions for solution is proved.

Asymptotic method of travelling wave solutions for a class of nonlinear reaction diffusion equation

Abstract In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.