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.
A class of singularly perturbed initial boundary value problems of reaction diffusion equations for the nonlinear boundary condition with two parameters is considered. Under suitable conditions, by using the theory of differential inequalities, the existence and the asymptotic behaviour of the solution for the initial boundary value problem are studied. The obtained solution indicates that there are initial and boundary layers and the thickness of the boundary layer is less than the thickness of the initial layer.
In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
A class of singularly perturbed boundary value problems of weakly non linear equation for fourth order on the interval [a, b] with two parameters is considered. Under suitable conditions, firstly, the reduced solution and formal outer solution are constructed using the expansion method of power series. Secondly, using the transformation of stretched variable, the first boundary layer corrective term near x = a is constructed which possesses exponential attenuation behavior. Then, using the stronger transformation of stretched variable, the second boundary layer corrective term near x = a is constructed, wtfich also possesses exponential attenuation behavior. The thickness of second boundary layer is smaller than the first one and forms a cover layer near x = a. Finally, using the theory of differential inequalities, the existence, uniform validity in the whole interval [a, b] and asymptotic behavior of solution for the original boundary value problem are proved. Satisfying results are obtained.
A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is constructed.And then,by using the theory of differential inequalities the uniformly validity of solution is proved.
This paper considers a class of boundary value problems for the semilinear singularly perturbed fractional differential equation. Under the suitable conditions, first, the outer solution of the original problem is obtained; secondly, using the stretched variable and the composing expansion method the boundary layer is constructed; finally, using the theory of differential inequalities the asymptotic behaviour of solution for the problem is studied and the uniformly valid asymptotic estimation is discussed.
This paper consider a class of perturbed mechanism for the western boundary undercurrents in the Pacific. The model of generalized governing equations is studied. Using the perturbation method, it constructs the asymptotic solution of the model. And the accuracy of asymptotic solution is proved by the theory of differential inequalities. Thus the uniformly valid asymptotic expansions of the solution are obtained.
This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method, it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homotopic mapping, it obtains an approximate solution with an arbitrary degree of accuracy for the solitary wave. From the approximate solution obtained by using the homotopic mapping method, it possesses a good accuracy.
In this paper, the nonlocal nonlinear reaction-diffusion singularly perturbed problems with two parameters are studied. Using a singular perturbation method, the structure of the solutions to the problem is discussed in relation to two small parameters. The asymptotic solutions of the problem are given.
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.
