Related papers: Multi-dark soliton solutions of the two-dimensiona…
Dark solitons have been observed in optical systems (optical fibres, dielectric guides and bulk media), and, more recently, in harmonically confined atomic Bose-Einstein condensates. This paper presents an overview of some of the common…
In this paper, we demonstrate the emergence of non-degenerate bright solitons and summarize their several interesting features in a completely integrable two-component long-wave-short-wave resonance interaction model with a general form of…
The fast dynamics of molecular polaritonics is scrutinized theoretically through the implementation of two-dimensional spectroscopy protocols. We derive conceptually simple and computationally efficient formulas to calculate two-dimensional…
We analytically study plasma solitary waves, or solitons, in a two-dimensional (2D) electron system (ES) placed in close proximity to and between two ideal metallic gates. As a rule, solitons are described using a perturbative approach…
The algebraic geometric approach to $N$-component systems of nonlinear integrable PDE's is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink…
We search for static solitons stabilized by heavy fermions in a 3+1 dimensional Yukawa model. We compute the renormalized energy functional, including the exact one-loop quantum corrections, and perform a variational search for…
Some aspects of the multidimensional soliton geometry are considered. It is shown that some simples (2+1)-dimensional equations are exact reductions of the Self-Dual Yang-Mills equation or its higher hierarchy.
The increasing technological control of two-dimensional materials has allowed the demonstration of 2D lateral junctions, which display unique properties that might serve as the basis for a new generation of 2D electronic and optoelectronic…
Nonlocal reductions of a nonisospectral (2+1)-dimensional breaking soliton Ablowitz-Kaup-Newell-Segur equation are discussed on the base of double Wronskian reduction technique. Various types of solutions, including soliton solutions and…
Acoustic solitons obtained through a reductive perturbation scheme are normally governed by a Korteweg-de Vries (KdV) equation. In multispecies plasmas at critical compositions the coefficient of the quadratic nonlinearity vanishes.…
Interaction properties of complex solitons are studied for the two U(1)-invariant integrable generalizations of the mKdV equation, given by the Hirota equation and the Sasa-Satsuma equation, which share the same travelling wave…
The formation and propagation of small amplitude Heavy-ion-acoustic (HIA) solitary waves and double layers in an unmagnetized collisionless multi-component plasma system consisting of superthermal electrons, Boltzmann distributed light…
In the present contribution, we explore a host of different stationary states, namely dark-bright solitons and their lattices, that arise in the context of multi-component atomic Bose-Einstein condensates. The latter, are modeled by systems…
Novel soliton structures are constructed for the Fokas-Lenells equation. In so doing, and after discussing the stability of continuous waves, a multiple scales perturbation theory is used to reduce the equation to a Korteweg-de Vries system…
We study the influences to the discrete soliton (DS) by introducing linearly long-range nonlocal interactions, which give rise to the off-diagonal elements of the linearly coupled matrix in the discrete nonlinear schrodinger equation to be…
We introduce one- and two-dimensional (1D and 2D) models of parity-time ($% \mathcal{PT}$) -symmetric couplers with the mutually balanced linear gain and loss applied to the two cores, and cubic-quintic (CQ) nonlinearity acting in each one.…
We unravel the existence and stability properties of dark soliton solutions as they extend from the regime of trapped quantum droplets towards the Thomas-Fermi limit in homonuclear symmetric Bose mixtures. Leveraging a phase-plane analysis,…
We present a series of quantum states that are characterized by dark solitons of the nonlinear Schr\"{o}dinger equation (i.e. the Gross-Pitaevskii equation) for the one-dimensional (1D) Bose gas interacting through the repulsive…
We construct static solutions to a SU(2) Yang--Mills (YM) dilaton model in 4+1 dimensions subject to bi-azimuthal symmetry. The YM sector of the model consists of the usual YM term and the next higher order term of the YM hierarchy, which…
In this article we will develop some techniques aimed at the strong couplings in two-dimensional wave-Klein-Gordon system. We distinguish the roles of different type of decay factors and develop a method which permits us to "exchange" one…