Homotopic mapping solving method for gain fluency of a laser pulse amplifier

Abstract

The model for gain fluency of a laser pulse amplifier is studied. Using the homotopic mapping method, firstly, the system of the original model is packed up standardization; secondly, introducing a homotopic mapping, taking the property of the mapping, inducing a contrived parameter, the solving of a nonlinear problem translates into the solving of a linear problem. Then the approximate expressions of the solution for the corresponding model are obtained. And the precision for the approximate solution is compared. It illuminates that the obtained approximate solution using the homotopic mapping method possesses higher approximate degree. At one time, the expansion of solution through the homotopic mapping method can be kept in the analytic operation. Thus it also enables us through differential and integral operations to obtain other physics behavior for the gain fluency of laser pulse amplifier. nonlinear, homotopic mapping, laser pulse amplifierThe laser pulse amplifier is a very attractive object of study in modern physics. It is an important project of manufacture for the famous China-II laser pulse amplifier [1][2][3][4] . In this investigation, we need to understand many physical behaviors, such as gain fluency, pulse undulance, density of photon, density of energy, gain of energy and so on. Lately, there has been more profound study for the without wasting laser pulse amplifier. But for the wasting laser pulse amplifier, there is lesser study [1,2] . There is difficulty that the exact solution of nonlinear differential equation can not obtained generally. Thus the numerical simulated or asymptotic method is used to obtain approximate solution. But we cannot use the analytic operation for the numerical simulated solution. It possesses determinate localization. On the other hand, we can use analytic operation by using the asymptotic method. And the homotopic map is a good asymptotic method.Recently, many scholars have investigated the approximate theory [3][4][5] . Asymptotic methods have been developed and refined, including the method of averaging boundary layer method, matched asymptotic expansion method and multiple scales method. Using the asymptotic method, Mo et al. [6][7][8][9][10][11][12][13][14][15][16][17] considered also a class of singularly perturbed problems. In this paper, commencing the model of a class of laser pulse amplifier, by using the simple and valid homotopic mapping method [18] , we can rapidly solve for the approximate analytic solution with higher precision. And then it provides further study of the physics behavior of laser pulse amplifier.

The Solitary Wave Solution for Quantum Plasma Nonlinear Dynamic Model

“…Mo and others [18][19][20][21][22][23][24][25][26] have also discussed a class of nonlinear physical problems by means of some asymptotic analysis methods.…”

Approximate solution for mechanism of thermally and wind-driven ocean circulation

“…Approximate methods have been developed and improved, including the method of averaging, the boundary layer method, the matched asymptotic expansion method, and the multiple scales method (Dawes and Proctor, 2008;Graef and Kong, 2008;Hovhannisyan and Vulanovic, 2008;Ramos, 2009). Using the perturbation method, Mo et al studied some of nolinear perturbation problems (Mo et al, 2004;2007a;2007b;Mo and Wang, 2007;Mo and Lin, 2008a;2008b;2008c;Mo, 2009a;2009b;2009c). In this paper, we discuss a model of the thermally and wind-driven ocean circulation and obtain an approximate solution of the model by using the homotopic mapping perturbation method.…”

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.…”