Related papers: Resonance structures in coupled two-component $\ph…
We study the $\phi^{6}$ model and derive two broad classes of lattice discretizations that admit static, translationally invariant kinks; that is, stationary kink profiles that can be centered at an arbitrary position relative to the…
In order to identify the exact criteria for the formation of two-ring structures in galaxies, we studied the issue of gravitational instability of the corresponding structural vibration modes against the background of a composite disk model…
We report results of systematic numerical analysis of collisions between two and three stable dissipative solitons in the two-dimensional (2D) complex Ginzburg- Landau equation (CGLE) with the cubic-quintic (CQ) combination of gain and loss…
We determine the semiclassical energy levels for the \phi^4 field theory in the broken symmetry phase on a 2D cylindrical geometry with antiperiodic boundary conditions by quantizing the appropriate finite--volume kink solutions. The…
Soliton molecules may be formed in some possible mechanisms in both theoretical and experimental aspects. In this letter, we introduce a new possible mechanism, the velocity resonant, to form soliton molecules. Under the resonant mechanism,…
We extend the well-known theoretical treatment of the spontaneous symmetry breaking (SSB) in two-component systems, combining linear coupling and self-attractive nonlinearity, to a system in which the linear coupling competes with repulsive…
Using numerical simulations of the full nonlinear equations of motion we investigate topological solitons of a modified O(3) sigma model in three space dimensions, in which the solitons are stabilized by the Hopf charge. We find that for…
The paper deals with the interaction between buckling and resonance instabilities of mechanical systems. Taking into account the effect of geometric nonlinearity in the equations of motion through the geometric stiffness matrix, the problem…
We study the formation and collision of one- and two-dimensional (1D and 2D) Gaussian-shaped and flat-top (FT) solitons in the framework of the nonlinear Schr\"{o}dinger equation with the cubic-quintic nonlinearity and two intersecting…
The reconnection processes of 3-solitons with 2-resonance can produce distinct local structures that initially connect two pairs of V-shaped branches, then disappear, and later re-emerge as new forms. We call such local structures as stem…
We study boundary scattering in the $\phi^4$ model on a half-line with a one-parameter family of Neumann-type boundary conditions. A rich variety of phenomena is observed, which extends previously-studied behaviour on the full line to…
We use a recently constructed linearized soliton sector perturbation theory to calculate the form factors relevant to the elastic scattering of ultrarelativistic mesons off of nonrelativistic kinks. Both localized kink wave packets and also…
We study (2+1)-dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents, and demonstrate that these solitary waves exhibit a symmetry-breaking instability provided their total…
The aim of this work is to establish a linear instability result of stationary, kink and kink/anti-kink soliton profile solutions for the sine-Gordon equation on a metric graph with a structure represented by a $\mathcal Y$-junction. The…
We explore a variant of the $\phi^6$ model originally proposed in Phys.\ Rev.\ D {\bf 12}, 1606 (1975) as a prototypical, so-called, "bag" model in which domain walls play the role of quarks within hadrons. We examine the steady state of…
Semiconductor $p^+ - p^- - n - p^+ - n^{++}$ structures with large junction and contact areas are treated as 1 \times 2-dimensional active media, in which self-organized pattern formation can be expected. The local bistable behavior of the…
We report on numerical predictions and experimental observations of a novel type of temporal localized dissipative structures that manifest themselves in the self-defocusing regime of driven nonlinear optical resonators with two…
We introduce a two-dimensional (2D) system, which can be implemented in dual-core planar optical couplers with the Kerr nonlinearity in its cores, making it possible to blend effects of the PT symmetry, represented by the balanced linear…
This study deals with a piecewise $\phi^2$ scalar field theory in $(1+1)$ dimensions. The scalar field potential is designed with a triple-well shape, engendering kink solutions with asymmetric square-well linearized potentials. Thus, the…
We study the scattering processes of kink-antikink and kink-kink pairs in a field theory model with non-differentiable potential at its minima. The kink-antikink scattering includes cases of capture and escape of the soliton pair separated…