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研究了一个激光脉冲放大器增益通量的模型.利用同伦映射方法,首先对原模型系统作了规范整理,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.并且对近似解作了精度的比较,说明了用同伦映射方法得到的近似解具有较高的近似度.同时可以看出,同伦映射方法不同于一般的数值计算方法,它是一个解析的方法.因此通过同伦映射解,还可以对它继续进行解析运算,从而还可以进行微分和积分运算去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.
A model of gain gain of laser pulse amplifier is studied.Using homotopy mapping method, the original model system is first normalized and then a homotopy mapping is introduced.And then using the properties of the mapping, an artificial parameter is introduced to solve the nonlinearity The problem is transformed into solving a series of linear problems, and then the solutions of the corresponding linear problems are obtained one by one. Finally, the approximate expansion of the original model solution is obtained, and the accuracy of the approximate solutions is compared, which shows that the homotopic mapping method It can be seen that the homotopy mapping method is different from the general numerical calculation method and it is an analytical method, so the homotopic mapping solution can still carry out analytic operation on it, Thus, differential and integral operations can be performed to obtain the behavior of other physical quantities related to the gain of the laser pulse amplifier.