| Abstract: |
| In recent years, considerable attention has been devoted to nonlinear systems featuring a spatially nonlocal nonlinear response. In such systems, the nonlinear response at a point in space depends on the field values in a surrounding region. Here, we study nonlocal nonlinear Schr\odinger (NLS) models describing the evolution of optical beams in thermal optical media, nematic liquid crystals, and plasmas. We use multiscale expansion methods to asymptotically reduce the nonlocal NLS to completely integrable models arising in the theory of water waves, such as the Korteweg--de Vries (KdV), the Boussinesq/Benney--Luke, the Kadomtsev--Petviashvili (KP-I and KP-II), the Davey--Stewartson (DS-I and DS-II), and the Mel{\cprime}nikov systems. We show that the strength of nonlocality plays a role analogous to surface tension and thus strongly affects the types of solitons that can form in nonlocal media, as well as their stability and interactions. |
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