Singularly perturbed solution of coupled model in atmosphere-ocean for global climate

Abstract

A box model of the interhemispheric thermohaline circulation (THC) in atmosphere-ocean for global climate is considered. By using the multi-scales method, the asymptotic solution of a simplified weakly nonlinear model is discussed. Firstly, by introducing first scale, the zeroth order approximate solution of the model is obtained. Secondly, by using the multi-scales, the first order approximate equation of the model is found. Finally, second order approximate equation is formed to eliminate the secular terms, and a uniformly valid asymptotic expansion of solution is decided. The multi-scales solving method is an analytic method which can be used to analyze operation sequentially. And then we can also study the diversified qualitative and quantitative behaviors for corresponding physical quantities. This paper aims at providing a valid method for solving a box model of the nonlinear equation.

Approximate Solution of Homotopic Mapping to Solitary Wave for Generalized Nonlinear KdV System

“…Recently, many scholars such as Ni and Wei, [14] Bartier, [15] Llibre and de Silva [16] and Guarguaglini and Natalini [17] have carried out a great deal of work. Using the method of differential inequalities and others, researchers also considered a class of reaction diffusion problems, [18] activator inhibitor systems, [19] ecological environment, [20] shock wave, [21] soliton wave, [22,23] laser pulse, [24] ocean science, [25,26] atmospheric physics, [27−30] etc. In this Letter, we consider a class of generalized nonlinear KdV systems, and obtain approximate solution of solitary wave.…”

A class of boundary value problems for third-order differential equation with a turning point

“…Recently, many scholars such as Ni and Wei [2] , Bartier [3] , Libre et al [4] , and Guarguaglini and Natalini [5] have done much work. Using the method of differential inequalities and others, Mo et al considered also a class of reaction diffusion problems [6] , the shock wave [7] , the soliton wave [8][9][10][11] , the laser pulse [12][13] , the ocean science [14][15][16] , and the atmospheric physics [17][18][19] , etc. In this paper, using a special method, we construct a class of singularly perturbed differential equation boundary value problems with a turning point.…”

Asymptopic solution for a class of semilinear singularly perturbed fractional differential equation

“…Using the method of differential inequalities and others Mo et al considered also a class of singularly perturbed nonlinear boundary value problems for the reaction diffusion equations, [8] a class of activator inhibitor systems, [9] the ecological environment, [10] the shock wave, [11] the soliton, [12−16] the laser pulse, [17] the ocean science [18,19] and the problems of atmospheric physics. [20,21] In this paper, we constructed asymptotic solution for a class of fractional differential equation, and proved that the asymptotic solution is uniformly valid.…”