Solitons In Nonlocal Nonlinear Kerr Media With Exponential Response Fuction

Now in the changing society, science and technology are important parts of the human life, and gradually become the first productive forces. So in the modern science and technology, the nonlinear science which is the study of the nature of the nonlinear phenomena subject becomes the our popular research. With the deepening of the research for nonlinear science, nonlinear optical sub-ject for a light beam manipulate another beam light or automatic control of beam light gradually establish and perfect by people. Even, people find optical spatial soliton is an efficient path to make it come true. Because of the balance be-tween nonlinearity and diffraction, spatial optical solitons will keep their shapes when they are propagating. In recent years, due to their particle-like nature on propagations and interactions, studies on optical spatial soliton never reduce. Because of been found in different media, optical spatial soliton can be divided into different soliton. Due to their numerous novel properties, the study about nonlocal spatial solitons becomes a hot research in the soliton area. Snyder and Mitchell find the nonlocal nonlinearity response in the nonlocal nonlinearity re-sponse media in1997. In contrast to local media, the nonlinear refractive index response in nonlocal media, at a center point is not determined solely by the wave intensity at that point, but also depends on the other wave intensity in its vicin-ity. The study of various kinds of nonlocal solitons have promoted the all-optical switching and optical interconnection devices, also provided theoretical support for further understanding of spatial solitons and nonlinear scienceIn our paper, we study the nonlocal nonlinear kerr media with exponential response fuction. As far as we know, such equations have been already studied by the numerical method. It is well known that it is non-integrable system, so it is difficult to find the exact solutions analytically.In this paper, we use the classical Lie-group method and similarity transformations.First, we find some exact analytical solutions including bright soliton solution, dipole-mode soliton solution, double soliton solution and periodic solution when a slit laser beam propagates in Kerr-type nonlinear, nonlocal media with exponential response function. Furthermore, we address the energy flow is a monotonically growing function of l2and the Hamiltonian decreases while the energy flow increases. And we also obtain an Airy-like soliton by numerical method. Then, we study the nonlocal medium with optical lattices. We construct explicit solutions of nonlin-ear Schrodinger equations by using similarity transformations, and we get some analytical solutions including bright resonant solitons and breathing solitons.