A Study On The Mathematical Model Of Raman Scattering With Small Perturbation

Raman scattering is based on the inelastic light scattering effect distributed symmetrically on both sides of Rayleigh scattering light after the interaction between light and matter.Raman spectroscopy can be used to quickly and harmlessly analyze the composition and structure of matter.Therefore,it is of great significance for the study of Raman scattering.In this paper,the mathematical model of Raman scattering with small perturbation is studied,and the theoretical method and the numerical method are discussed.In theory,based on the Banach fixed point theorem,this paper proves the existence and uniqueness of the solution of the initial value problem by means of the integral equation method.Then,the first term of the asymptotic solution is obtained by the multiple scale method.Finally,the method of integral equation is combined with the Granville inequality to fully verify the uniform validity of the first term of the asymptotic solution.In numerical method,with the aid of matlab software to draw out the numerical solution and the approximate solution of the image,found that the numerical solution and approximate solution fitting is better,in order to more intuitive see that the error between the numerical solution and the approximate solution,plotted the logarithm of the maximum difference(error)between the numerical solution and the approximate solution with the logarithm of ε2,image,also calculate the ratio between error and ε2.Both methods show that error satisfies O ε2,which means the uniform validity of the asymptotic solution obtained is further demonstrated by numerical method.