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Asymptotic reductions of a defocusing nonlocal nonlinear Schr{o}dinger model in $(3+1)$-dimensions, in both Cartesian and cylindrical geometry, are presented. First, at an intermediate stage, a Boussinesq equation is derived, and then its far-field, in the form of a variety of Kadomtsev-Petviashvilli (KP) equations for right- and left-going waves, is found. KP models includ
We study coupled unstaggered-staggered soliton pairs emergent from a system of two coupled discrete nonlinear Schr{o}dinger (DNLS) equations with the self-attractive on-site self-phase-modulation nonlinearity, coupled by the repulsive cross-phase-mod
In this paper we analyze the existence, stability, dynamical formation and mobility properties of localized solutions in a one-dimensional system described by the discrete nonlinear Schr{o}dinger equation with a linear point defect. We consider both
We study the transverse instability and dynamics of bright soliton stripes in two-dimensional nonlocal nonlinear media. Using a multiscale perturbation method, we derive analytically the first-order correction to the soliton shape, which features an
We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSY--QM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of reflectionless H
We derive a straightforward variational method to construct embedded soliton solutions of the third-order nonlinear Schodinger equation and analytically demonstrate that these solitons exist as a continuous family. We argue that a particular embedded