Variational and accessible soliton approximations to multidimensional solitons in highly nonlocal nonlinear media

Abstract

We apply the variational approach to solitons in highly nonlocal nonlinear media in D = 1, 2, 3 dimensions. We compare results obtained by the variational approach with those obtained in the accessible soliton approximation, by considering the same system of equations in the same spatial region and under the same boundary conditions. To assess the accuracy of these approximations, we also compare them with the numerical solution of the equations. We discover that the variational highly nonlocal approximation provides more accurate results and as such is more appropriate solution than the accessible soliton approximation.

Dark matter condensates as highly nonlocal solitons: instability in the Schwarzschild metric and laboratory analog

“…We note that the nonlocal nature of the gravitational self-interaction guarantees the stability of the localized mass distribution as proved in [20]. Under these conditions, we can apply the HNA [21]. The HNA replaces the nonlocal nonlinear potential generated by a Gaussian mass distribution with a parabolic potential.…”

“…The HNA replaces the nonlocal nonlinear potential generated by a Gaussian mass distribution with a parabolic potential. The starting point of the HNA exposed in [21] is the same of our work, equations ( 1) and ( 2). Thus, we can directly apply their results.…”

Comment on “Spatial optical solitons in highly nonlocal media”

“…But this crucial result was published before in [7] and [10]. None of the papers [7,10,11], where these and other related matters were discussed priorly, were cited in any of the papers by the above group. In addition, some questions remain unanswered, concerning recent work by the group.First, it is unclear why AS approximation cannot deal with highly nonlocal situations, i.e.…”

“…Thus, in crucial characteristics, the AS approximation is an oversimplification that at best can only qualitatively apply to solitons in highly nonlocal media. The first published accurate quantitative correction to AS approximation was presented in [7], direct comparison between AS theory and VA was given in [10], while a complete comparison in D=1,2,3 spatial dimensions can be found in [11].In [4], published after our papers [7] and [10], Alberucci et al discussed the main features of ASs in realistic diffusive self-focusing media. Authors concluded that "the highly nonlocal (AS) model does not accurately describe the soliton and predicts for it a width roughly √ 2 smaller than the actual size.…”

“…Thus, in crucial characteristics, the AS approximation is an oversimplification that at best can only qualitatively apply to solitons in highly nonlocal media. The first published accurate quantitative correction to AS approximation was presented in [7], direct comparison between AS theory and VA was given in [10], while a complete comparison in D=1,2,3 spatial dimensions can be found in [11].…”