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In pattern-forming systems, localized patterns are states of intermediate complexity between fully extended ordered patterns and completely irregular patterns. They are formed by stationary fronts enclosing an ordered pattern inside an…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…
Shell structure in the single particle spectrum of deformed harmonic oscillator potentials when a term proportional to $(\vec L)^2$ is added is analyzed for a large particle number. A scaling law which gives a dividing line between regular…
We address necklace solitons supported by circular waveguide arrays with out-of-phase modulation of nonlinearity and linear refractive index. Such two-dimensional necklace solitons appear as rings of multiple out-of-phase bright spots. We…
We address surface soliton complexes formed at the edge of annular guiding structures containing several concentric rings. Such soliton complexes feature a -phase difference between neighboring spots. It is shown that the multipole-mode…
General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta E_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability…
It is commonly held that a necessary condition for the existence of solitons in nonlinear-wave systems is that the soliton's frequency (spatial or temporal) must not fall into the continuous spectrum of radiation modes. However, this is not…
Based on a microscopic model, we develop a continuum description for a suspension of microscopic self propelled particles. With this continuum description we study the role of long-range interactions in destabilizing macroscopic ordered…
A narrow energy band of the electronic spectrum in some direction in low-dimensional crystals may lead to a negative differential conductance and N-shaped I-V curve that results in an instability of the uniform stationary state. A…
We show that an inhomogeneous defocusing nonlinearity that grows toward the periphery in the positive and negative transverse directions at different rates can support strongly asymmetric fundamental and multipole bright solitons, which are…
We study the vibrational motion of membrane resonators upon strong drive in the strongly nonlinear regime. By imaging the vibrational state of rectangular siliconnitride membrane resonators and by analyzing the frequency response using…
We investigate the stability of possible order parameter configurations in clean layered heterostructures of the $SFS...FS$ type, where $S$ is a superconductor and $F$ a ferromagnet. We find that for most reasonable values of the geometric…
We show that multipole solitons can be made stable via vectorial coupling in bulk nonlocal nonlinear media. Such vector solitons are composed of mutually incoherent nodeless and multipole components jointly inducing a nonlinear refractive…
Frequency stability is key to performance of nanoresonators. This stability is thought to reach a limit with the resonator's ability to resolve thermally-induced vibrations. Although measurements and predictions of resonator stability…
We consider a network of interacting resonators and analyze the physical ingredients that enable the emergence of relaxation-free and decoherence-free subspaces. We investigate two different situations: i) when the whole network interacts…
Symbiotic vortex-bright soliton structures with non-trivial topological charge in one component are found to be robust in immiscibel two-component superfluids, due to the effective potential created by a stable vortex in the other…
The problem of the stability of a nonlinear thermomagnetic wave with respect to small thermal and electromagnetic perturbations in hard superconductors was studied. It is shown that spatially bounded solutions may correspond only to the…
Based on micromagnetic simulations, we report on a novel helical magnetic structure in a soft magnetic film that is sandwiched between and exchange-coupled to two hard magnetic layers. Confined between antiparallel hard magnetic moments, a…
Stable embedded solitons are discovered in the generalized third-order nonlinear Schroedinger equation. When this equation can be reduced to a perturbed complex modified KdV equation, we developed a soliton perturbation theory which shows…
We analyze photo-refractive incoherent soliton beams and their interactions in Kerr-like nonlinear media. The field in each of M incoherently interacting components is calculated using an integrable set of coupled nonlinear Schrodinger…