Exact Solutions and Numerical Solutions of Equations Describing Photovoltaic Photorefractive Media with an External Electric Field
|School||Zhejiang Normal University|
|Keywords||Classical Lie method Photovoltaic photorefractive Soliton|
In recent years, since the first experimental observation of the photorefractive spatial solitons , photorefractive spatial solitons have been the focus of considerable attention . So far, it has been predicted and proved the existence of four types of scalar photorefractive spatial solitons : quasi- steady-state soliton , screening soliton , photovoltaic solitons and screening photovoltaic solitons . The latter three are stable solitons . Recently, the applied electric field of photovoltaic photorefractive crystals attract more interest. Screening photovoltaic solitons are diffracted beam and the photovoltaic effect and exterior spaces non- uniform electric field shielding effect in the balance generated by nonlinear effects . In fact, the screening soliton and photovoltaic solitons in a closed condition is a special case of screening photovoltaic solitons . Therefore, screening soliton and photovoltaic solitons can be incorporated into photovoltaic photorefractive solitons . The main difference between them is : one is the applied electric field , and the other is in the photovoltaic crystals add background lighting. In this paper, classical Lie group method to study the electric field of photovoltaic photorefractive crystal evolution equations . Until now, many people use numerical methods studied this work and get bright photovoltaic photorefractive solitons , dark solitons , and gray soliton solutions , but also on the characteristics of these solitons were studied . However , these results are rarely accurate analytical solution . Classical Lie method is to look for non- integrable system is an effective means of analytical solutions . Our work system theory pointed out the electric field of photovoltaic photorefractive crystal evolution equations numerical soliton solutions only exist , but also gives some exact analytical solution , and the physical meaning of these solutions are discussed .