High-order Nonautonomous Schrodinger Equation Of Freak Wave Mechanics And Baseband Modulation Instability

With the development of modern science and technology,nonlinear science became the modern science and technology development of a new logo,nonlinear science penetrated into all disciplines and fields,such as geophysics,ocean and weather prediction,fluid mechanics,nonlinear optics,plasma,etc.Soliton as an important branch of nonlinear science,has a broad applicability,the majority of scholars attention.A very important in the process of nonlinear scientific research work,is the solution of the nonlinear problem.There are a number of solutions of nonlinear partial differential equations.Among them,the most decomposition can better describe the physical problems,but most of this kind of nonlinear equations are variable coefficient equation and want to get the accurate solution of nonlinear equations is very difficult.It is only stay in the level of the numerical solution.Schrodinger equation with variable coefficients,and its deformation form is considered to be the most widely applied mathematics m odel,it can be derived from maxwell's equations,in numerous neighborhood has extremely important position.So far,there have been many kinds of methods of solving nonlinear Schrodinger equation of constant coefficient,for the nonlinear Schrodinger equation with variable coefficients,the method to get the exact soliton solutions,it remains to be further research and discussion.This article mainly around the high-order non-autonomous type Schrodinger equation of freak wave mechanics study and baseband modulation instability,content mainly includes the following aspects:(1)introducing the origin,development and current status of optical soliton,the forming mechanism of soliton,and several kinds of effective methods for solving the soliton.(2)using the methods of similarity transformation,the higher-order nonlinear Schrodinger equation with variable coefficients,is studied(vc-HNLS)under the background of continuous wave of nonautonomous soliton solution of the situation,and the compression effect of third-order dispersion coefficient of soliton,including constant,trigonometric function,exponential function,and a function's influence on soliton.(3)when the third-order dispersion coefficient structure for the special period,and select appropriate modulation amplitude and frequency modulation structure.We also analyzed the structure of the nature of space,the study found that when the modulation amplitude,into a structure.(4)the light pulse width reaches femtosecond magnitude,need to consider the higher-order effects(third-order dispersion,nonlinear dispersion,since ACTS forms and gain(loss),etc.).At this time,the nonlinear schrodinger equation into a high order nonlinear Hirota equation.This article simply introduces the modulation instability,and by using the method of linear stability analysis,high order variable coefficient is studied Hirota equation of modulation instability.(5)the research results of this article has carried on the brief summarizati on,and made some prospects of research work.