激光脉冲放大器增益通量耦合系统解

冯依虎; 陈怀军; 莫嘉琪

doi:10.21656/1000-0887.370208

激光脉冲放大器增益通量耦合系统解

doi: 10.21656/1000-0887.370208

¹亳州学院电子与信息工程系, 安徽亳州 236800;²安徽师范大学数学计算机科学学院, 安徽芜湖 241003

基金项目: 国家自然科学基金(41275062;11202106)；安徽省教育厅自然科学基金(KJ2015A347;KJ2017A702)；安徽省高校优秀青年人才支持计划重点项目(gxyqZD2016520)

详细信息

作者简介:
冯依虎（1982—），男，副教授，硕士(E-mail: fengyihubzsz@163.com)；莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

中图分类号: O175.29
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出版历程
- 收稿日期: 2016-07-05
- 修回日期: 2016-12-01
- 刊出日期: 2017-07-15

Solutions to the Gain Flux Coupling System of Laser Pulse Amplifiers

¹Department of Electronics and Information Engineering, Bozhou College, Bozhou, Anhui 236800, P.R.China;²School of Mathematics & Computer Science, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

Funds: The National Natural Science Foundation of China(41275062;11202106)

摘要

摘要: 研究了一个激光脉冲放大器增益通量系统解的问题.首先讨论了较一般的系统, 然后引入一个同伦映射.再利用映射的性质, 引进一个人工参数, 将求解非线性问题转化为求解一系列线性问题.再逐次地求出对应的线性问题的解, 最后得到了原模型解的近似展开式.可以看出, 同伦映射方法是一个解析的方法.它是通过函数的解析运算并用初等函数来表达近似解，其不同于用离散数值运算的数值计算方法.因此通过同伦映射解, 还可以对它继续进行解析运算, 从而可以进行微分和积分等运算来得到与激光脉冲放大器增益通量相关的其他物理量的性态.
- 激光 /
- 放大器 /
- 非线性
Abstract: The solutions to the gain flux coupling system of laser pulse amplifiers were studied. Firstly, the system of the general model was discussed; secondly, the homotopic mapping was used and an artificial parameter was introduced with the property of the mapping, to transform the nonlinear problem to a series of linear problems, which were solved one by one. Then the approximate expressions of the solutions to the corresponding model were obtained. The expansion of solutions with the homotopic mapping method is analytic, where the analytic operations of the functions are kept and the approximate solutions are expressed with elementary functions, which are different from the numrically computed discrete solutions and can be further analytically computed. Thus the differential and integral operations can be implemented to obtain other physical behaviors of the gain flux for laser pulse amplifiers.
- laser /
- amplifier /
- nonlinear

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参考文献(25)

[1]	唐立家, 蔡希洁, 林尊琪. “神光Ⅱ”主放大器中的波形控制[J]. 物理学报, 2001,50(6): 1075-1079.(TANG Li-jia, CAI Xi-jie, LIN Zun-qi. Control of pulse shape in “Shengguang Ⅱ” main amplifers[J]. Acta Physica Sinica,2001,50(6): 1075-1079.(in Chinese))
[2]	刘仁红, 蔡希洁, 杨琳, 等. 激光脉冲放大器的增益通量曲线研究[J]. 物理学报, 2005,54(7): 3140-3143.(LIU Ren-hong, CAI Xi-jie, YANG Lin, et al. Study on gain fluence curve of a laser pulse amplifier[J]. Acta Physica Sinica,2005,54(7): 3140-3143.(in Chinese))
[3]	NI Wei-ming, WEI Jun-cheng. On positive solutions concentrating on spheres for the Gierer-Meinhardt system[J]. Journal of Differential Equations,2006,221(1): 158-189.
[4]	Bartier J P. Global behavior of solutions of a reaction-diffusion equation with gradient absorption in unbounded domains[J]. Asymptotic Analysis,2006,46(3/4): 325-347.
[5]	Khasminskii R Z, Yin G. Limit behavior of two-time-scale diffusion revisited[J]. Journal of Differential Equations,2005,212(1): 85-113.
[6]	MO Jia-qi. Homotopic mapping solving method for gain fluency of a laser pulse amplifier[J]. Science in China Series G: Physics, Mechanics and Astronomy,2009,52(7): 1007-1010.
[7]	MO Jia-qi. Singular perturbation for a class of nonlinear reaction diffusion systems[J]. Science in China (Series A),1989,32(11): 1306-1315.
[8]	MO Jia-qi, LIN Wan-tao. Asymptotic solution for a class of sea-air oscillator model for El Nio-southern oscillation[J]. Chinese Physics B,2008,17(2): 370-372.
[9]	Amiraligev G M.On difference schemes for problems of the theory of dispersive waves[J].Soviet Math Dokl,1991,42:235~238.
[10]	MO Jia-qi, LIN Shu-rong. The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation[J]. Chinese Physics B,2009,18(9): 3628-3631.
[11]	MO Jia-qi, CHEN Xian-feng. Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation[J]. Chinese Physics B,2010,19(10): 100203.
[12]	MO Jia-qi. Solution of travelling wave for nonlinear disturbed long-wave system[J]. Communications in Theoretical Physics,2011,55(3): 387-390.
[13]	MO Jia-qi, LIN Wan-tao, LIN Yi-hua. Asymptotic solution for the El Nio time delay sea-air oscillator model[J]. Chinese Physics B,2011,20(7): 070205.
[14]	莫嘉琪. 扰动Vakhnenko方程物理模型的行波解[J]. 物理学报, 2011,60(9): 090203.(MO Jia-qi. Travelling wave solution of disturbed Vakhnenko equation for physical model[J]. Acta Physica Sinica,2011,60(9): 090203.(in Chinese))
[15]	莫嘉琪, 程荣军, 葛红霞. 具有控制项的弱非线性发展方程行波解[J]. 物理学报, 2011,60(5): 050204.(MO Jia-qi, CHENG Rong-jun, GE Hong-xia. Travelling wave solution of the weakly nonlinear evolution equation with control term[J]. Acta Physica Sinica,2011,60(5): 050204.(in Chinese))
[16]	莫嘉琪. 一类非线性尘埃等离子体孤波解[J]. 物理学报, 2011,60(3): 030203.(MO Jia-qi. The solution for a class of nonlinear solitary waves in dusty plasma[J]. Acta Physica Sinica,2011,60(3): 030203.(in Chinese))
[17]	FENG Yi-hu, MO Jia-qi. The shock asymptotic solution for nonlinear elliptic equation with two parameters[J]. Mathematica Applicata,2015,27(3): 579-585.
[18]	冯依虎, 石兰芳, 汪维刚, 等. 一类广义非线性强阻尼扰动发展方程的行波解[J]. 应用数学和力学, 2015,36(3): 315-324.(FENG Yi-hu, SHI Lan-fang, WANG Wei-gang, et al. Travelling wave solution to a class of generalized nonlinear strong-damp disturbed evolution equations[J]. Applied Mathematics and Mechanics,2015,36(3): 315-324.(in Chinese))
[19]	冯依虎, 莫嘉琪. 一类非线性非局部扰动LGH方程的孤子行波解[J]. 应用数学和力学, 2016,37(4): 426-433.(FENG Yi-hu, MO Jia-qi. Soliton travelling wave solutions to a class of nonlinear nonlocal disturbed LGH equations[J]. Applied Mathematics and Mechanics,2016,37(4): 426-433.(in Chinese))
[20]	FENG Yi-hu, MO Jia-qi. Asymptotic solution for singularly perturbed fractional order differential equation[J]. Journal of Mathematics,2016,36(2): 239-245.
[21]	FENG Yi-hu, CHEN Xian-feng, MO Jia-qi. The generalized interior shock layer solution of a class of nonlinear singularly perturbed reaction diffusion problem[J]. Mathematica Applicata,2016,29(1): 161-165.
[22]	LIAO Shi-jun. Beyond Perturbation: Introduction to the Homotopy Analysis Method [M]. New York: CRC Press Co, 2004.
[23]	LIAO Shi-jun. Homotopy Analysis Method in Nonlinear Differential Equations [M]. Heidelberg: Springer & Higher Education Press, 2012.
[24]	de Jager E M, JIANG Fu-ru. The Theory of Singular Perturbation [M]. Amsterdam: North-Holland Publishing Co, 1996.
[25]	Barbu L, Morosanu G. Singularly Perturbed Boundary-Value Problems [M]. Basel: Birkhauserm Verlag AG, 2007.