Applications of spectral renormalization method to the research of nonlocal optical spatial soliton

We use spectral renormalization method to solve the nonlocal nonlinear Schrdinger equation, which gives accurate waveform of nonlocal optical spatial soliton. The relation between critical power and critical beamwidth is acquired in different nonlocal conditions. We discovered that optical spatial soliton exists stably in any nonlocal degree. Comparing analytic solution with numerical solution for different response functions, we find that they are consistent only under strong nonlocal and weak nonlocal conditions. The effective range of analytic solution is also given.