Pattern Formation and Solitons
Soliton and breather solutions of the nonlinear Schr\"odinger equation (NLSE) are known to model localized structures in nonlinear dispersive media such as on the water surface. One of the conditions for an accurate propagation of such…
Recently, we have shown that the Manakov equation can admit a more general class of nondegenerate vector solitons, which can undergo collision without any intensity redistribution in general among the modes, associated with distinct wave…
We observe and analyze formation, decay, and subsequent regeneration of ring-shaped clusters of (2+1)-dimensional spatial solitons (filaments) in a medium with the cubic-quintic (focusing-defocusing) self-interaction and strong dissipative…
In this work, a systematic study, examining the propagation of periodic and solitary wave along the magnetic field in a cold collision-free plasma, is presented. Employing the quasi-neutral approximation and the conservation of momentum…
We present a case study elaborating on the multiplicity and self-similarity of homoclinic and heteroclinic bifurcation structures in the 2D and 3D parameter spaces of a nonlinear laser model with a Lorenz-like chaotic attractor. In a…
We predict and observed novel highly anisotropic magnetic patterns obtained in the model of frustrated planar interacting magnetic moments (the classical $X-Y$ model) on the regular kagome lattice. The frustration is provided by the…
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the…
We demonstrate that fractional cubic-quintic nonlinear Schr\"odinger equation,characterized by its L\'evy index, maintains ring-shaped soliton clusters ("necklaces") carrying orbital angular momentum. They can be built, in the respective…
Under investigation is a new (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. The main results are listed as follows: (i) lump solutions; (ii) Interaction solutions between lump wave and solitary waves; (iii) Interaction solutions…
In this paper, a generalized (3 + 1)-dimensional variable-coefficient nonlinear-wave equation is studied in liquid with gas bubbles. Based on the Hirota's bilinear form and symbolic computation, lump and interaction solutions between lump…
In this paper, a variable-coefficient Boiti-Leon-Manna-Pempinelli equation is to be investigated. We obtain abundant multi-wave, breather wave and lump solutions by using the three waves method, the homoclinic breather approach and the…
We consider the wave propagation in media with step-like inhomogeneities. We choose two different protocols: (I) a step-like spatial dependence of the coupling constant that physically corresponds to the junction of two systems and (II) the…
Spectral singularities and the coherent perfect absorption are two interrelated concepts that have originally been introduced and studied for linear waves interacting with complex potentials. In the meantime, the distinctive asymptotic…
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…
We consider the asymmetric transmission properties of a Discrete Nonlinear Schr{\"o}dinger type dimer with a saturable nonlinear intersite coupling between the dimer sites, in addition to a cubic onsite nonlinearity and asymmetric linear…
Numerical simulations demonstrate a link between dynamically cold initial solutions and an evolution towards self-similarity. However the nature of this link is not fully understood. In this work the link between cold initial conditions and…
Mutual interaction of localized nonlinear waves, e.g. solitons and modulation instability patterns, is a fascinating and intensively-studied topic of nonlinear science. In this research report, we report on the observation of a novel type…
In this paper, the trial function method is employed to find the exact solutions for high-order nonlinear Schr\"odinger equations with time-dependent coefficients. This system describes the propagation of ultrashort light pulses in…
Equations of the Loewner class subject to non-constant boundary conditions along the real axis, are formulated and solved giving the geodesic paths of slits growing in the upper half complex plane. The problem is motivated by Laplacian…
Localized coherent structures can form in externally-driven dispersive optical cavities with a Kerr-type nonlinearity. Such systems are described by the Lugiato-Lefever equation, which supports a large variety of dynamical solutions. Here,…