Variational approach versus accessible soliton approximation in nonlocal, nonlinear media

Abstract

We discuss differences between the variational approach to solitons and the accessible soliton approximaion in a highly nonlocal, nonlinear medium. We compare results of both approximations by considering the same system of equations in the same spatial region, under the same boundary conditions. We also compare these approximations with the numerical solution of the equations. We find that the variational highly nonlocal approximation provides more accurate results and, as such, is a more appropriate solution than the accessible soliton approximation. The accessible soliton model offers a radical simplification in the treatment of highly nonlocal, nonlinear media, with easy comprehension and convenient parallels to a quantum harmonic oscillator, however, with a hefty price tag: a systematic numerical discrepancy of up to 100% with the numerical results.