Calculation of the transmission wave of a laser pulse amplifier

Abstract

A nonlinear transmission system for the laser pulse amplifier is discussed. Using the generalized functional-variational iteration theory and method, the corresponding approximate solution of the system is obtained, which facilitates the design of laser pulse amplifiers.

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

“…where 𝑢 0 and 𝑣 0 are represented by Eqs. ( 23) and (24), respectively. Using the Fourier transform method, a set of solution of system ( 25)-( 26) with zero initial value will read…”

“…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.…”

Homotopic mapping solving method of the reduces equation for Kelvin waves

“…Recently, many scholars such as Guarguaglini, [3] Hovhannisyan and Vulanovic, [4] Abid, Jieli and Trabelsi, [5] Graef and Kong, [6] and Barbu and Cosma [7] have done a great deal of work. Using the method of differential inequalities, Mo et al also considered a class of singularly perturbed nonlinear boundary value problems for the reaction diffusion equations, [8] the activator inhibitor systems, [9] the ecological environment, [10] the shock wave, [11] the soliton, [12−15] the laser pulse, [16] the ocean science [17,18] and atmospheric physics. [19−23] In this paper, using a special homotopic mapping method, we study the Kelvin waves in atmospheric physics.…”

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

“…Recently, many scholars such as Guarguaglini and Natalini, [3] Hovhannisyan and Vulanovic, [4] Abid, Jieli and Trabelsi, [5] Graef and Kong [6] and Barbu and Cosma [7] have done a great deal of works. 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.…”