Related papers: Multi-dark soliton solutions for the multi-compone…
This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schr\"odinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics.…
In this work, we will use inverse scattering transform to study the semi-discrete Gardner equation under two types of non-vanishing boundary conditions, and investigate two interesting nonlinear waves in the presence of discrete spectrum,…
We study the stability, form and interaction of single and multiple dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates. The solitons are found numerically as stationary solutions in the moving frame of a non-local…
We consider two-component solitons in a medium with a periodic modulation of the nonlinear coefficient. The modulation enables the existence of complex multihump vector states. In particular, vector solitons composed of dipole and…
Solitons are universal nonlinear excitations that appear in settings as varied as optics, water waves, and quantum gases [1-5]. While reduced models of soliton dynamics are well established, their validity and dynamical behaviour in…
We report on the controlled creation of multiple soliton complexes of the dark-bright type in one-dimensional two-component, three-component and spinor Bose-Einstein condensates. The formation of these states is based on the so-called…
An overview is given of basic models combining discreteness in their linear parts (i.e. the models are built as dynamical lattices) and nonlinearity acting at sites of the lattices or between the sites. The considered systems include the…
We investigate the transverse instability of two-component solitons forming in a planar waveguide operating in the regime of strong light-matter coupling. The instability emerges as a result of the coupling between transverse diffraction of…
Dark solitons carrying quantized phase information arouse great interest in different nonlinear systems. A dark soliton in 1D can be stabilized in microcavity polariton condensates as a confinement is imposed on it to prevent its decay.…
We show that bimodal systems with a spatially nonuniform defocusing cubic nonlinearity, whose strength grows toward the periphery, can support stable two-component solitons. For a sufficiently strong XPM interaction, vector solitons with…
Two-dimensional gray solitons to the nonlinear Schroedinger equation are numerically created by two processes to show its robustness. One is transverse instability of a one-dimensional gray soliton, and another is a pair annihilation of a…
We predict that strong coupling between waveguide photons and excitons of quantum well embedded into waveguide results in the formation of hybrid dark and anti-dark light-matter solitons. Such temporal solitons exist due to interplay…
Two-component Bose-Einstein condensates in the miscible phase can support polarization solitary waves, known as magnetic solitons. By calculating the interaction potential between two magnetic solitons, we elucidate the mechanisms and…
Dark matter may form bound states in a dark sector with an attractive force between two dark matter particles. Searches for dark matter at colliders can differ dramatically from routine searches if bound states, dubbed darkonia, are…
We primarily study concave-downward and convex-upward types of elliptic dark soliton solutions for the Hirota equation, exhibiting a concave-downward shape on both upper and lower envelope surfaces and showing a convex-upward shape on the…
We consider an array of double oligomers in an optical waveguide device. A mathematical model for the system is the coupled discrete nonlinear Schr\"odinger (NLS) equations, where the gain-and-loss parameter contributes to the…
Bright plane soliton solutions of an integrable (2+1) dimensional ($n+1$)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a 3-wave system consisting of two short wave components and one…
We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schroedinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities.…
As is known, a solitary pulse in the complex cubic Ginzburg-Landau (GL) equation is unstable. We demonstrate that a system of two linearly coupled GL equations with gain and dissipation in one subsystem and pure dissipation in another…
One-parameter families of exact two-component solitary-wave solutions for interacting high-frequency (HF) and low-frequency (LF) waves are found in the framework of Zakharov-type models, which couple the nonlinear Schr\"odinger equation…