激光脉冲放大器增益通量耦合系统解

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.

Solutions to the Gain Flux Coupling System of Laser Pulse Amplifiers

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.