ar X iv : n lin / 0 60 70 62 v 3 [ nl in . P S ] 1 5 A ug 2 00 6 Two - dimensional nonlocal multisolitons

We study the bound states of two-dimensional bright solitons in nonlocal nonlin-ear media. The general properties and stability of these multisolitary structures are investigated analytically and numerically. We have found that a steady bound state of coherent nonrotating and rotating solitary structures (azimuthons) can exist above some threshold power. A dipolar nonrotating multisoliton occurs to be stable within the finite range of the beam power. Azimuthons turn out to be stable if the beam power exceeds some threshold value. The bound states of three or four nonrotating solitons appear to be unstable. The recent experimental observations of spatial solitons in nonlocal media such as nematic liquid crystals [1, 2], lead glasses [3], renewed an interest to coherent structures in spatially nonlocal nonlinear media. In the spatially nonlocal media the nonlinear response depends on the wave packet intensity at some extensive spatial domain. Nonlocality is a key feature of many nonlinear media. It naturally appears in different physical systems such as plasmas [4–6], Bose-Einstein condensates [7], optical media [8], liquid crystals [1], and soft matter [9]. Different types of single (solitons , vortices) and composite (soliton clusters) solitary structures have been predicted and experimentally observed in various nonlinear media [10]. Rotating scalar multipoles (azimuthons) were first introduced in Ref. [11] for models with local nonlinearity. A composite soliton structure, or a multi-soliton complex is a self-localized state which is a nonlinear superposition of several fundamental solitons. Stationary multi-soliton structures in nonlocal media were considered first in Refs. [12, 13]. However, a question of the stability of the multisolitons is still an open problem. In particular, the form of the nonlinear nonlocal response is crucial for the multisoliton stability. Stable two-dimensional (2D) rotating [14] and nonrotating [15] dipole solitons in a medium with Gaussian response function have been numerically observed. Authors of Refs. [16] investigated a more realistic model with the Helmholtz type response function (often referred to as the model with thermal nonlinearity) and showed that multipole vector solitons can be made stable. This model describes, in particular, the nonlinear nonlocal response of some thermo-optical materials, liquid crystals, and partially ionized plasmas [1, 3, 5]. Very recently experimental observation of scalar multipole solitons in the optical media with thermal nonlocal nonlinearity has been reported [17]. It is particularly remarkable that all multisolitons investigated in Ref. [17] are found to be unstable, but with a large parameters range where the instability is …