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We study the existence, formation and dynamics of gray solitons for an extended quintic nonlinear Schrodinger (NLS) equation. The considered model finds applications to water waves, when the characteristic parameter $kh$ - where $k$ is the wavenumber and $h$ is the undistorted waters depth - takes the critical value $kh=1.363$. It is shown that this model admits approximate dark soliton solutions emerging from an effective Korteweg-de Vries equation and that two types of gray solitons exist: fast and slow, with the latter being almost stationary objects. Analytical results are corroborated by direct numerical simulations.
Irrotational ow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrodinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by elliptic func
We present the study of the dark soliton dynamics in an inhomogenous fiber by means of a variable coefficient modified nonlinear Schr{o}dinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and linear gain/los
We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schrodinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe atomic Bose-Ein
In this work, we study solitary waves in a (2+1)-dimensional variant of the defocusing nonlinear Schrodinger (NLS) equation, the so-called Camassa-Holm NLS (CH-NLS) equation. We use asymptotic multiscale expansion methods to reduce this model to a Ka
Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional defocusing nonlinear Schrodinger (NLS) equation. This problem is of fundamental importance as a dispersive analogue of